scholarly journals Cohomological rigidity of oriented Hantzsche–Wendt manifolds

2016 ◽  
Vol 302 ◽  
pp. 1044-1068
Author(s):  
J. Popko ◽  
A. Szczepański
Keyword(s):  
Cohomological Rigidity

scholarly journals Properties of Bott manifolds and cohomological rigidity

2011 ◽  
Vol 11 (2) ◽  
pp. 1053-1076 ◽  
Author(s):  
Suyoung Choi ◽  
Dong Youp Suh
Keyword(s):  
Cohomological Rigidity

scholarly journals Strong cohomological rigidity of toric varieties

2017 ◽  
Vol 147 (5) ◽  
pp. 971-992
Author(s):  
Suyoung Choi ◽  
Seonjeong Park
Keyword(s):  
Betti Number ◽  
Cohomology Ring ◽  
Toric Varieties ◽  
Ring Isomorphism ◽  
Quasitoric Manifolds ◽  
Cohomological Rigidity

Every cohomology ring isomorphism between two non-singular complete toric varieties (respectively, two quasitoric manifolds), with second Betti number 2, is realizable by a diffeomorphism (respectively, homeomorphism).

scholarly journals Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

2021 ◽  
pp. 1-41
Author(s):  
DANIJELA DAMJANOVIĆ ◽  
JAMES TANIS
Keyword(s):  
Vector Fields ◽  
Smooth Vector ◽  
Local Rigidity ◽  
Cohomological Rigidity ◽  
Perturbative Result ◽  
The Way

Abstract In this paper we prove a perturbative result for a class of ${\mathbb Z}^2$ actions on Heisenberg nilmanifolds that have Diophantine properties. Along the way we prove cohomological rigidity and obtain a tame splitting for the cohomology with coefficients in smooth vector fields for such actions.

Cohomological rigidity of algebraic ℤd-actions

1995 ◽  
Vol 15 (4) ◽  
pp. 759-805 ◽  
Author(s):  
K. Schmidt
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Cohomology Group ◽  
Hölder Continuous ◽  
Cohomological Rigidity

AbstractWe prove that every Hölder-continuous cocycle for an expansive and mixing ℤd-action α by automorphisms of a compact, abelian group X is Hölder-cohomologous to an affine cocycle, and give a complete description of the Hölder cohomology group of α.

Infinitesimal rigidity of boundary lattice actions

1999 ◽  
Vol 19 (1) ◽  
pp. 35-60 ◽  
Author(s):  
A. KONONENKO
Keyword(s):  
Symmetric Spaces ◽  
Compact Type ◽  
Infinitesimal Rigidity ◽  
Duality Method ◽  
Cocompact Lattice ◽  
Higher Rank ◽  
Cocompact Lattices ◽  
Lattice Actions ◽  
Cohomological Rigidity ◽  
Twisted Cocycles

In Part 1 we describe a duality method for calculating twisted cocycles. In Part 2 we use our method to prove various results on cohomological rigidity of higher-rank cocompact lattice actions. In Part 3 we use the results of Parts 1 and 2 to prove infinitesimal rigidity of the actions of cocompact lattices on the maximal boundaries of some non-compact type symmetric spaces.

scholarly journals On the Equivalence of B-Rigidity and C-Rigidity for Quasitoric Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jin Hong Kim
Keyword(s):  
Convex Polytopes ◽  
Cohomology Rings ◽  
Toric Topology ◽  
Quasitoric Manifolds ◽  
Simple Convex ◽  
Cohomological Rigidity

For quasitoric manifolds and moment-angle complexes which are central objects recently much studied in toric topology, there are several important notions of rigidity formulated in terms of cohomology rings. The aim of this paper is to show that, among other things, Buchstaber-rigidity (or B-rigidity) is equivalent to cohomological-rigidity (or C-rigidity) for simple convex polytopes supporting quasitoric manifolds.

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