Čech Cohomology with Coefficients in a Topological Abelian Group

2015 ◽  
Vol 211 (1) ◽  
pp. 40-57
Author(s):  
L. Mdzinarishvili ◽  
L. Chechelashvili
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group ◽  
Cech Cohomology

scholarly journals Duality for topological abelian group stacks and T-duality

2009 ◽  
pp. 227-347 ◽  
Author(s):  
Ulrich Bunke ◽  
Thomas Schick ◽  
Markus Spitzweck ◽  
Andreas Thom
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group

scholarly journals Arcs in the Pontryagin dual of a topological abelian group

2015 ◽  
Vol 425 (1) ◽  
pp. 337-348 ◽  
Author(s):  
L. Außenhofer ◽  
M.J. Chasco ◽  
X. Domínguez
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group

scholarly journals Commutative Topological Semigroups Embedded into Topological Abelian Groups

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 87
Author(s):  
Julio César Hernández Arzusa
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Topological Semigroup ◽  
Abelian Groups ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Topological Semigroups ◽  
Topological Monoid

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.

scholarly journals A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible

2013 ◽  
Vol 56 (1) ◽  
pp. 213-217 ◽  
Author(s):  
Daniel V. Tausk
Keyword(s):  
Abelian Group ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Character Group ◽  
Divisible Abelian Group ◽  
Torsion Free

AbstractIt was claimed by Halmos in 1944 that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free, then G is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of G is both torsion free and divisible, it does not follow that G is divisible.

scholarly journals Pattern-equivariant cohomology with integer coefficients

2007 ◽  
Vol 27 (6) ◽  
pp. 1991-1998 ◽  
Author(s):  
LORENZO SADUN
Keyword(s):  
Abelian Group ◽  
Inverse Limit ◽  
Equivariant Cohomology ◽  
Representation Variety ◽  
Integer Coefficients ◽  
Easy Proof ◽  
Tiling Space ◽  
Cech Cohomology ◽  
Original Theorem ◽  
Limit Structure

AbstractWe relate Kellendonk and Putnam’s pattern-equivariant (PE) cohomology to the inverse-limit structure of a tiling space. This gives a version of PE cohomology with integer coefficients, or with values in any Abelian group. It also provides an easy proof of Kellendonk and Putnam’s original theorem relating PE cohomology to the Čech cohomology of the tiling space. The inverse-limit structure also allows for the construction of a new non-Abelian invariant, the PE representation variety.

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