Complete systems of invariant of m-tuples for fundamental groups of the two-dimensional Euclidian space

2020 ◽  
Vol 2020 (1) ◽  
pp. 57-84
Author(s):  
Djavvat Khadjiev ◽  
Shavkat Ayupov ◽  
Gayrat Beshimov
Keyword(s):  
Fundamental Groups ◽  
Two Dimensional ◽  
Euclidian Space

Tilings, fundamental cocycles and fundamental groups of symbolic ${\Bbb Z}^{d}$-actions

1998 ◽  
Vol 18 (6) ◽  
pp. 1473-1525 ◽  
Author(s):  
KLAUS SCHMIDT
Keyword(s):  
Finite Type ◽  
Homomorphic Image ◽  
Discrete Group ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Shift Spaces ◽  
Shift Space ◽  
Topologically Mixing

We prove that certain topologically mixing two-dimensional shifts of finite type have a ‘fundamental’ $1$-cocycle with the property that every continuous $1$-cocycle on the shift space with values in a discrete group is continuously cohomologous to a homomorphic image of the fundamental cocycle. These fundamental cocycles are closely connected with representations of the shift space by Wang tilings and the tiling groups of Conway, Lagarias and Thurston, and they determine the projective fundamental groups of the shift spaces introduced by Geller and Propp.

scholarly journals Thurston norms of tunnel number-one manifolds

2019 ◽  
Vol 28 (09) ◽  
pp. 1950056
Author(s):  
Natalia Pacheco-Tallaj ◽  
Kevin Schreve ◽  
Nicholas G. Vlamis
Keyword(s):  
Unit Ball ◽  
Special Class ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Thurston Norm ◽  
Tunnel Number

The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of three-manifolds [Formula: see text] with [Formula: see text], and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are three-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces.

STATISTICS AND SPIN ON TWO-DIMENSIONAL SURFACES

1991 ◽  
Vol 06 (30) ◽  
pp. 2801-2810 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
T. EINARSSON ◽  
T. R. GOVINDARAJAN ◽  
R. RAMACHANDRAN
Keyword(s):  
Braid Groups ◽  
Configuration Spaces ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Connected Sums

The fundamental groups of the configuration spaces for the O(3) nonlinear σ-model on the compact genus g surfaces [Formula: see text] and on the connected sums [Formula: see text] are known for any soliton number N. So are the braid for N spinless particles on these manifolds. The representations of these groups govern the possible statistics of solitons and particles. We show that when spin and creation/annihilation processes are introduced, the fundamental groups for the particles are the same as the corresponding σ-model groups. These fundamental groups incorporate the spin-statistics connection and are of greater physical relevance than the standard braid groups.

The projective fundamental group of a ℤ2-shift

1995 ◽  
Vol 15 (6) ◽  
pp. 1091-1118 ◽  
Author(s):  
William Geller ◽  
James Propp
Keyword(s):  
Topological Space ◽  
Fundamental Group ◽  
Topological Conjugacy ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Limit Group ◽  
Long Distance ◽  
Mixing Properties ◽  
Point Data ◽  
Factor Maps

AbstractWe define a new invariant for symbolic ℤ2-actions, the projective fundamental group. This invariant is the limit of an inverse system of groups, each of which is the fundamental group of a space associated with the ℤ2-action. The limit group measures a kind of long-distance order that is manifested along loops in the plane, and roughly speaking bears the same relation to the mixing properties of the ℤ2-action that π1; of a topological space bears to π0. The projective fundamental group is invariant under topological conjugacy. We calculate this invariant for several important examples of ℤ2-actions, and use it to prove non-existence of certain constant-to-one factor maps between two-dimensional subshifts. Subshifts that have the same entropy and periodic point data can have different projective fundamental groups.

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH GEOMETRICALLY TWO-DIMENSIONAL FUNDAMENTAL GROUPS

2009 ◽  
Vol 01 (02) ◽  
pp. 123-151 ◽  
Author(s):  
IAN HAMBLETON ◽  
MATTHIAS KRECK ◽  
PETER TEICHNER
Keyword(s):  
Fundamental Group ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Intersection Form

Closed oriented 4-manifolds with the same geometrically two-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w2-type, equivariant intersection form and the Kirby–Siebenmann invariant. As an application, we obtain a complete homeomorphism classification of closed oriented 4-manifolds with solvable Baumslag–Solitar fundamental groups, including a precise realization result.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Analysis of the 9th November 1990 flare

2000 ◽  
Vol 179 ◽  
pp. 229-232
Author(s):  
Anita Joshi ◽  
Wahab Uddin
Keyword(s):  
Image Processing ◽  
Two Dimensional ◽  
Temporal Behaviour ◽  
Contour Maps ◽  
Dimensional Measurements ◽  
Processing Software ◽  
Image Processing Software

AbstractIn this paper we present complete two-dimensional measurements of the observed brightness of the 9th November 1990Hαflare, using a PDS microdensitometer scanner and image processing software MIDAS. The resulting isophotal contour maps, were used to describe morphological-cum-temporal behaviour of the flare and also the kernels of the flare. Correlation of theHαflare with SXR and MW radiations were also studied.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

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