scholarly journals A homological characterization of abelian $B\sb 2$-groups

1994 ◽  
Vol 121 (2) ◽  
pp. 409-409
Author(s):  
K. M. Rangaswamy
Keyword(s):  
Homological Characterization

scholarly journals One-relator groups and algebras related to polyhedral products

2021 ◽  
pp. 1-20
Author(s):  
Jelena Grbić ◽  
George Simmons ◽  
Marina Ilyasova ◽  
Taras Panov
Keyword(s):  
Homology Group ◽  
Homotopy Theory ◽  
Commutator Subgroup ◽  
Homology Groups ◽  
Homological Characterization ◽  
One Relator Groups ◽  
Combinatorial Condition ◽  
The Moment ◽  
Necessary And Sufficient

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$ , we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal {R}_K$ , to be a one-relator group; and for the Pontryagin algebra $H_{*}(\Omega \mathcal {Z}_K)$ of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For $RC_K'$ , it is given by a condition on the homology group $H_2(\mathcal {R}_K)$ , whereas for $H_{*}(\Omega \mathcal {Z}_K)$ it is stated in terms of the bigrading of the homology groups of $\mathcal {Z}_K$ .

scholarly journals A homological characterization of topological amenability

2012 ◽  
Vol 12 (3) ◽  
pp. 1763-1776
Author(s):  
Jacek Brodzki ◽  
Graham Niblo ◽  
Piotr Nowak ◽  
Nick Wright
Keyword(s):  
Homological Characterization

scholarly journals A Note on Fine Graphs and Homological Isoperimetric Inequalities

2016 ◽  
Vol 59 (01) ◽  
pp. 170-181 ◽  
Author(s):  
Eduardo Martínez-Pedroza
Keyword(s):  
Isoperimetric Inequality ◽  
Isoperimetric Inequalities ◽  
Positive Answer ◽  
Cell Complex ◽  
Conjugacy Classes ◽  
Homological Characterization ◽  
Simply Connected ◽  
Relative Hyperbolicity ◽  
Dimensional Cell

Abstract In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected 2-complex X with a linear homological isoperimetric inequality, a bound on the length of attachingmaps of 2-cells, and finitely many 2-cells adjacent to any edge must have a fine 1-skeleton. We provide a positive answer to this question. We revisit a homological characterization of relative hyperbolicity and show that a group G is hyperbolic relative to a collection of subgroups P if and only if G acts cocompactly with ûnite edge stabilizers on a connected 2-dimensional cell complex with a linear homological isoperimetric inequality and P is a collection of representatives of conjugacy classes of vertex stabilizers.

A homological characterization of Krull domains II

2019 ◽  
Vol 47 (5) ◽  
pp. 1917-1929
Author(s):  
Fanggui Wang ◽  
Lei Qiao
Keyword(s):  
Homological Characterization ◽  
Krull Domains
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