scholarly journals Polynomially weighted $\ell^p$-completions and group homology

2020 ◽  
Vol 4 (1) ◽  
pp. 87-109
Author(s):  
Alexander Engel ◽  
Clara Löh
Keyword(s):  
Group Homology

The mapping class group: Homology and linearity

2005 ◽  
pp. 43-51
Author(s):  
A. Montorsi ◽  
M. Rasetti
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Group Homology

o-MINIMAL FUNDAMENTAL GROUP, HOMOLOGY AND MANIFOLDS

2002 ◽  
Vol 65 (02) ◽  
pp. 257-270 ◽  
Author(s):  
ALESSANDRO BERARDUCCI ◽  
MARGARITA OTERO
Keyword(s):  
Fundamental Group ◽  
Group Homology

scholarly journals Group homology and extensions of groups

2008 ◽  
Vol 10 (1) ◽  
pp. 237-257 ◽  
Author(s):  
Ioannis Emmanouil ◽  
Inder Bir S. Passi
Keyword(s):  
Group Homology

scholarly journals -invisibility and a class of local similarity groups

2014 ◽  
Vol 150 (10) ◽  
pp. 1742-1754 ◽  
Author(s):  
Roman Sauer ◽  
Werner Thumann
Keyword(s):  
Unitary Representation ◽  
Local Similarity ◽  
Group Homology ◽  
Thompson’S Group ◽  
Reduced Group ◽  
Generalized Zero ◽  
Similarity Groups

AbstractIn this note we show that the members of a certain class of local similarity groups are ${l}^{2}$-invisible, i.e. the (non-reduced) group homology of the regular unitary representation vanishes in all degrees. This class contains groups of type ${F}_{\infty }$, e.g. Thompson’s group $V$ and Nekrashevych–Röver groups. They yield counterexamples to a generalized zero-in-the-spectrum conjecture for groups of type ${F}_{\infty }$.

scholarly journals Propagating sharp group homology decompositions

2006 ◽  
Vol 200 (2) ◽  
pp. 525-538 ◽  
Author(s):  
Jesper Grodal ◽  
Stephen D. Smith
Keyword(s):  
Group Homology

scholarly journals A limit approach to group homology

2008 ◽  
Vol 319 (4) ◽  
pp. 1450-1461 ◽  
Author(s):  
Ioannis Emmanouil ◽  
Roman Mikhailov
Keyword(s):  
Group Homology

scholarly journals Homology of SL2 over function fields I: Parabolic subcomplexes

2018 ◽  
Vol 2018 (739) ◽  
pp. 159-205
Author(s):  
Matthias Wendt
Keyword(s):  
Vector Bundles ◽  
Function Fields ◽  
Equivalence Classes ◽  
Isotropy Group ◽  
Closed Field ◽  
Explicit Formulas ◽  
Algebraically Closed Field ◽  
Group Homology ◽  
Equivariant Homology ◽  
Smooth Affine

Abstract The present paper studies the group homology of the groups {\operatorname{SL}_{2}(k[C])} and {\operatorname{PGL}_{2}(k[C])} , where {C=\overline{C}\setminus\{P_{1},\dots,P_{s}\}} is a smooth affine curve over an algebraically closed field k. It is well known that these groups act on a product of trees and the quotients can be described in terms of certain equivalence classes of rank two vector bundles on the curve {\overline{C}} . There is a natural subcomplex consisting of cells with suitably non-trivial isotropy group. The paper provides explicit formulas for the equivariant homology of this “parabolic subcomplex”. These formulas also describe group homology of {\operatorname{SL}_{2}(k[C])} above degree s, generalizing a result of Suslin in the case {s=1} .

scholarly journals Narain Gupta's three normal subgroup problem and group homology

2019 ◽  
Vol 526 ◽  
pp. 243-265
Author(s):  
Roman Mikhailov ◽  
Inder Bir S. Passi
Keyword(s):  
Normal Subgroup ◽  
Group Homology ◽  
Subgroup Problem

scholarly journals K-groups of rings and the homology of their elementary matrix groups

1985 ◽  
Vol 38 (2) ◽  
pp. 268-274
Author(s):  
Janet Aisbett
Keyword(s):  
Commutative Ring ◽  
Matrix Group ◽  
Elementary Matrix ◽  
Matrix Groups ◽  
Group Homology ◽  
Low Dimensional

AbstractLow dimensional algebraic K-groups of a commutative ring are described in terms of the homology of its elementary matrix group. This approach is prompted by recent successful computations of low-dimensional K-groups using group homology methods, and it builds on the identity K2(R)=H2(ER).

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