Congruence Link Complements—A 3-Dimensional Rademacher Conjecture

2018 ◽  
pp. 177-200
Author(s):  
M. D. Baker ◽  
A. W. Reid
Keyword(s):  
3 Dimensional ◽  
Link Complements

scholarly journals Representation Homology of Topological Spaces

2020 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C Ramadoss ◽  
Wai-Kit Yeung
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Hochschild Homology ◽  
Topological Spaces ◽  
Free Loop Space ◽  
3 Dimensional ◽  
Complex Projective Spaces ◽  
Link Complements ◽  
Representation Varieties ◽  
Complex Projective

Abstract In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology parallel to the Loday–Pirashvili construction of higher Hochschild homology; in fact, we establish a direct geometric relation between the two theories by proving that the representation homology of the suspension of a (pointed connected) space is isomorphic to its higher Hochschild homology. We also construct some natural maps and spectral sequences relating representation homology to other homology theories associated with spaces (such as Pontryagin algebras, ${{\mathbb{S}}}^1$-equivariant homology of the free loop space, and stable homology of automorphism groups of f.g. free groups). We compute representation homology explicitly (in terms of known invariants) in a number of interesting cases, including spheres, suspensions, complex projective spaces, Riemann surfaces, and some 3-dimensional manifolds, such as link complements in ${\mathbb{R}}^3$ and the lens spaces $ L(p,q) $. In the case of link complements, we identify the representation homology in terms of ordinary Hochschild homology, which gives a new algebraic invariant of links in ${\mathbb{R}}^3$.

LINK COMPLEMENTS ARISING FROM ARITHMETIC GROUP ACTIONS

1995 ◽  
Vol 06 (03) ◽  
pp. 337-370 ◽  
Author(s):  
FRITZ GRUNEWALD ◽  
ULRICH HIRSCH
Keyword(s):  
Quotient Space ◽  
Free Subgroup ◽  
Arithmetic Group ◽  
Hyperbolic Structure ◽  
3 Dimensional ◽  
Ring Of Integers ◽  
Hyperbolic Volume ◽  
Link Complements ◽  
Torsion Free Subgroup ◽  
Torsion Free

Let [Formula: see text] be a torsion-free subgroup acting discontinuously on 3-dimensional hyperbolic space [Formula: see text]. Assume further that Γ\ℍ3 has finite hyperbolic volume. The quotient-space Γ\ℍ3 is then a 3-manifold which can be compactified by the addition of finitely many 2-tori. This paper discusses a procedure which decides whether Γ\ℍ3 is homeomorphic to the complement of a link in S3. We apply our procedure to subgroups of low index in [Formula: see text], where [Formula: see text] is the ring of integers in [Formula: see text]. As a result we find new link complements having a complete hyperbolic structure coming from an arithmetic group. Finally we prove that up to conjugacy there are only finitely many commensurability classes of arithmetic subgroups [Formula: see text] so that Γ\ℍ3 is homeomorphic to the complement of a link in S3.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

Deviations from Ideal Decagonal Symmetry in Electron Diffraction Patterns of the “Decagonal” Phase in the Al-Co-Cu Alloy System

1991 ◽  
Vol 49 ◽  
pp. 914-915
Author(s):  
Atul S. Ramani ◽  
Earle R. Ryba ◽  
Paul R. Howell
Keyword(s):  
Electron Microscope ◽  
Alloy System ◽  
Nominal Composition ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Decagonal Phase ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Lattice Periodicity ◽  
Diffraction Patterns

The “decagonal” phase in the Al-Co-Cu system of nominal composition Al65CO15Cu20 first discovered by He et al. is especially suitable as a topic of investigation since it has been claimed that it is thermodynamically stable and is reported to be periodic in the dimension perpendicular to the plane of quasiperiodic 10-fold symmetry. It can thus be expected that it is an important link between fully periodic and fully quasiperiodic phases. In the present paper, we report important findings of our transmission electron microscope (TEM) study that concern deviations from ideal decagonal symmetry of selected area diffraction patterns (SADPs) obtained from several “decagonal” phase crystals and also observation of a lattice of main reflections on the 10-fold and 2-fold SADPs that implies complete 3-dimensional lattice periodicity and the fundamentally incommensurate nature of the “decagonal” phase. We also present diffraction evidence for a new transition phase that can be classified as being one-dimensionally quasiperiodic if the lattice of main reflections is ignored.

A Novel Reconstitution Method for Inducing the Formation of Regular 2-Dimensional Arrays of Membrane Proteins and Lipids

1988 ◽  
Vol 46 ◽  
pp. 152-153 ◽  
Author(s):  
A. Engel ◽  
A. Holzenburg ◽  
K. Stauffer ◽  
J. Rosenbusch ◽  
U. Aebi
Keyword(s):  
Membrane Proteins ◽  
Flow Rate ◽  
Lipid Membranes ◽  
Functional Characterization ◽  
Dimensional Structure ◽  
Electron Crystallography ◽  
Peltier Element ◽  
Protein Ratio ◽  
Precise Control ◽  
3 Dimensional

Reconstitution of solubilized and purified membrane proteins in the presence of phospholipids into vesicles allows their functions to be studied by simple bulk measurements (e.g. diffusion of differently sized solutes) or by conductance measurements after transformation into planar membranes. On the other hand, reconstitution into regular protein-lipid arrays, usually forming at a specific lipid-to-protein ratio, provides the basis for determining the 3-dimensional structure of membrane proteins employing the tools of electron crystallography.To refine reconstitution conditions for reproducibly inducing formation of large and highly ordered protein-lipid membranes that are suitable for both electron crystallography and patch clamping experiments aimed at their functional characterization, we built a flow-dialysis device that allows precise control of temperature and flow-rate (Fig. 1). The flow rate is generated by a peristaltic pump and can be adjusted from 1 to 500 ml/h. The dialysis buffer is brought to a preselected temperature during its travel through a meandering path before it enters the dialysis reservoir. A Z-80 based computer controls a Peltier element allowing the temperature profile to be programmed as function of time.

Structure and Interaction of Protamine by Dark Field Electron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 160-161
Author(s):  
D.P. Bazett-Jones ◽  
F.P. Ottensmeyer
Keyword(s):  
Electron Microscopy ◽  
Dark Field ◽  
Amino Acid Sequences ◽  
Dimensional Structure ◽  
3 Dimensional ◽  
Field Electron ◽  
Proposed Model ◽  
Field Electron Microscopy ◽  
Dark Field Electron ◽  
Positively Charged

It has been shown for some time that it is possible to obtain images of small unstained proteins, with a resolution of approximately 5Å using dark field electron microscopy (1,2). Applying this technique, we have observed a uniformity in size and shape of the 2-dimensional images of pure specimens of fish protamines (salmon, herring (clupeine, Y-l) and rainbow trout (Salmo irideus)). On the basis of these images, a model for the 3-dimensional structure of the fish protamines has been proposed (2).The known amino acid sequences of fish protamines show stretches of positively charged arginines, separated by regions of neutral amino acids (3). The proposed model for protamine structure (2) consists of an irregular, right-handed helix with the segments of adjacent arginines forming the loops of the coil.

Design and calibration of an IVEM for general 3-dimensional imaging of non-diffracting materials

1992 ◽  
Vol 50 (2) ◽  
pp. 1040-1041
Author(s):  
Neil Rowlands ◽  
Jeff Price ◽  
Michael Kersker ◽  
Seichi Suzuki ◽  
Steve Young ◽  
...  
Keyword(s):  
3D Imaging ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
3 Dimensional ◽  
3D Microstructure ◽  
Image Translation ◽  
Digital Correlation ◽  
On Line ◽  
Mechanical Stage ◽  
Projection Angle

Three-dimensional (3D) microstructure visualization on the electron microscope requires that the sample be tilted to different positions to collect a series of projections. This tilting should be performed rapidly for on-line stereo viewing and precisely for off-line tomographic reconstruction. Usually a projection series is collected using mechanical stage tilt alone. The stereo pairs must be viewed off-line and the 60 to 120 tomographic projections must be aligned with fiduciary markers or digital correlation methods. The delay in viewing stereo pairs and the alignment problems in tomographic reconstruction could be eliminated or improved by tilting the beam if such tilt could be accomplished without image translation.A microscope capable of beam tilt with simultaneous image shift to eliminate tilt-induced translation has been investigated for 3D imaging of thick (1 μm) biologic specimens. By tilting the beam above and through the specimen and bringing it back below the specimen, a brightfield image with a projection angle corresponding to the beam tilt angle can be recorded (Fig. 1a).

4-dimensional, high-resolution imaging of living cells

1992 ◽  
Vol 50 (1) ◽  
pp. 416-417
Author(s):  
Shinya Inoué
Keyword(s):  
Light Microscope ◽  
Living Cells ◽  
Live Cells ◽  
Video Tape ◽  
Active Living ◽  
High Resolution Imaging ◽  
3 Dimensional ◽  
Dynamic Architecture ◽  
Resolution Imaging ◽  
Disk Memory

This paper reports progress of our effort to rapidly capture, and display in time-lapsed mode, the 3-dimensional dynamic architecture of active living cells and developing embryos at the highest resolution of the light microscope. Our approach entails: (A) real-time video tape recording of through-focal, ultrathin optical sections of live cells at the highest resolution of the light microscope; (B) repeat of A at time-lapsed intervals; (C) once each time-lapsed interval, an image at home focus is recorded onto Optical Disk Memory Recorder (OMDR); (D) periods of interest are selected using the OMDR and video tape records; (E) selected stacks of optical sections are converted into plane projections representing different view angles (±4 degrees for stereo view, additional angles when revolving stereos are desired); (F) analysis using A - D.

High resolution spot scan imaging of frozen, hydrated actin bundles with 400kV electrons

1992 ◽  
Vol 50 (1) ◽  
pp. 512-513
Author(s):  
J. Jakana ◽  
M.F. Schmid ◽  
P. Matsudaira ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Binding Proteins ◽  
Actin Binding ◽  
Eukaryotic Cells ◽  
Dimensional Structure ◽  
Structural Basis ◽  
Actin Bundle ◽  
Actin Bundles ◽  
3 Dimensional ◽  
Macromolecular Assembly

Actin is a protein found in all eukaryotic cells. In its polymerized form, the cells use it for motility, cytokinesis and for cytoskeletal support. An example of this latter class is the actin bundle in the acrosomal process from the Limulus sperm. The different functions actin performs seem to arise from its interaction with the actin binding proteins. A 3-dimensional structure of this macromolecular assembly is essential to provide a structural basis for understanding this interaction in relationship to its development and functions.

Sign in / Sign up

Export Citation Format

Share Document