scholarly journals The spectrum of simplicial volume of non-compact manifolds

2021 ◽  
Author(s):  
Nicolaus Heuer ◽  
Clara Löh
Keyword(s):  
Compact Manifolds ◽  
Simplicial Volume ◽  
Locally Finite ◽  
Open Manifolds ◽  
Low Dimensional

AbstractWe show that, in dimension at least 4, the set of locally finite simplicial volumes of oriented connected open manifolds is $$[0,\infty ]$$ [ 0 , ∞ ] . Moreover, we consider the case of tame open manifolds and some low-dimensional examples.

Complexity of shadows and traversing flows in terms of the simplicial volume

2016 ◽  
Vol 08 (03) ◽  
pp. 501-543 ◽  
Author(s):  
Gabriel Katz
Keyword(s):  
Compact Manifolds ◽  
Connected Components ◽  
Fundamental Groups ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Simplicial Volume ◽  
Localization Technique ◽  
Close Relatives ◽  
Universal Bounds

We combine Gromov’s amenable localization technique with the Poincaré duality to study the traversally generic vector flows on smooth compact manifolds [Formula: see text] with boundary. Such flows generate well-understood stratifications of [Formula: see text] by the trajectories that are tangent to the boundary in a particular canonical fashion. Specifically, we get lower estimates of the numbers of connected components of these flow-generated strata of any given codimension. These universal bounds are basically expressed in terms of the normed homology of the fundamental groups [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the double of [Formula: see text]. The norm here is the Gromov simplicial semi-norm in homology. It turns out that some close relatives of the normed homology spaces [Formula: see text], [Formula: see text] form obstructions to the existence of [Formula: see text]-convex traversally generic vector flows on [Formula: see text].

End Behaviour and Ergodicity for Homeomorphisms of Manifolds with Finitely Many Ends

1987 ◽  
Vol 39 (2) ◽  
pp. 473-491 ◽  
Author(s):  
S. Alpern ◽  
V. Prasad
Keyword(s):  
Significant Role ◽  
Smooth Manifold ◽  
Borel Measure ◽  
Compact Manifolds ◽  
Countable Union ◽  
Noncompact Manifold ◽  
Compact Open Topology ◽  
Locally Finite ◽  
Ergodic Properties ◽  
Answering Questions

The recent paper of Berlanga and Epstein [5] demonstrated the significant role played by the “ends” of a noncompact manifold M in answering questions relating homeomorphisms of M to measures on M. In this paper we show that an analysis of the end behaviour of measure preserving homeomorphisms of a manifold also leads to an understanding of some of their ergodic properties, and allows results previously obtained for compact manifolds to be extended (with qualifications) to the noncompact case. We will show that ergodicity is typical (dense Gδ) with respect to various compact-open topology closed subsets of the space consisting of all homeomorphisms of a manifold M which preserve a measure μ. It may be interesting for topologists to note that we prove when M is a σ-compact connected n-manifold, n≧ 2, then M is the countable union of an increasing family of compact connected manifolds. If M is a PL or smooth manifold, this is well known and easy. If M is just, however, a topological n-manifold then we apply the recent results [9] and [12] to prove the result. The Borel measure μ, is taken to be nonatomic, locally finite, positive on open sets, and zero for the manifold boundary of M.

scholarly journals Simplicial volume of compact manifolds with amenable boundary

2014 ◽  
Vol 07 (01) ◽  
pp. 23-46 ◽  
Author(s):  
Sungwoon Kim ◽  
Thilo Kuessner
Keyword(s):  
Fundamental Group ◽  
Finite Volume ◽  
Compact Manifold ◽  
Riemannian Metric ◽  
Compact Manifolds ◽  
Simplicial Volume ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Path Component ◽  
Proportionality Principle

Let M be the interior of a connected, oriented, compact manifold V of dimension at least 2. If each path component of ∂V has amenable fundamental group, then we prove that the simplicial volume of M is equal to the relative simplicial volume of V and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on M whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume.

Weak Mixing Manifold Homeomorphisms Preserving an Infinite Measure

1987 ◽  
Vol 39 (6) ◽  
pp. 1475-1488
Author(s):  
Steve Alpern ◽  
Vidhu Prasad
Keyword(s):  
Compact Manifold ◽  
Finite Measure ◽  
Compact Manifolds ◽  
Weak Mixing ◽  
Locally Finite ◽  
Infinite Measure ◽  
Finite Measures

Let denote the group of all homeomorphisms of a σ-compact manifold which preserve a σ-finite, nonatomic, locally positive and locally finite measure μ. In two recent papers [4, 5] the possible ergodicity of a homeomorphism h in was shown to be related to the homeomorphism h* induced by h on the ends of M. An end of a manifold is, roughly speaking, a distinct way of going to infinity. Those papers demonstrated in particular that always contains an ergodic homeomorphism, paralleling the similar result of Oxtoby and Ulam [11] for compact manifolds with finite measures. Unfortunately the techniques used in [4] and [5] rely on the fact that a skyscraper construction with an ergodic base transformation is ergodic, a result which cannot be extended to finer properties than ergodicity.

Thermoelectric Properties of PbSr(Se,Te)-Based Low Dimensional Structures

2000 ◽  
Vol 626 ◽  
Author(s):  
Harald Beyer ◽  
Joachim Nurnus ◽  
Harald Böttner ◽  
Armin Lambrecht ◽  
Lothar Schmitt ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermoelectric Properties ◽  
Power Factor ◽  
Evaluation Method ◽  
Interband Transition ◽  
Multiple Quantum Well ◽  
Calculated Data ◽  
Multiple Quantum ◽  
Ir Transmission ◽  
Low Dimensional

ABSTRACTThermoelectric properties of low dimensional structures based on PbTe/PbSrTe-multiple quantum-well (MQW)-structures with regard to the structural dimensions, doping profiles and levels are presented. Interband transition energies and barrier band-gap are determined from IR-transmission spectra and compared with Kronig-Penney calculations. The influence of the data evaluation method to obtain the 2D power factor will be discussed. The thermoelectrical data of our layers show a more modest enhancement in the power factor σS2 compared with former publications and are in good agreement with calculated data from Broido et al. [5]. The maximum allowed doping level for modulation doped MQW structures is determined. Thermal conductivity measurements show that a ZT enhancement can be achieved by reducing the thermal conductivity due to interface scattering. Additionally promising lead chalcogenide based superlattices for an increased 3D figure of merit are presented.

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