Classification of hermitian forms and semisimple groups over fields of virtual cohomological dimension one

1996 ◽  
Vol 89 (1) ◽  
pp. 373-394 ◽  
Author(s):  
Claus Scheiderer
Keyword(s):  
Cohomological Dimension ◽  
Semisimple Groups ◽  
Hermitian Forms ◽  
Dimension One ◽  
Virtual Cohomological Dimension

scholarly journals Free and Properly Discontinuous Actions of Groups on Homotopy 2n-spheres

2018 ◽  
Vol 61 (2) ◽  
pp. 305-327
Author(s):  
Marek Golasiński ◽  
Daciberg Lima Gonçalves ◽  
Rolando Jimenez
Keyword(s):  
Free Group ◽  
Cyclic Group ◽  
Cohomological Dimension ◽  
Direct Products ◽  
Orbit Spaces ◽  
Homotopy Types ◽  
Finite Dimensional ◽  
The Family ◽  
Dimension One ◽  
Virtual Cohomological Dimension

Let G be a group acting freely, properly discontinuously and cellularly on some finite dimensional CW-complex Σ(2n) which has the homotopy type of the 2n-sphere 𝕊2n. Then, that action induces a homomorphism G → Aut(H2n(Σ(2n))). We classify all pairs (G, φ), where G is a virtually cyclic group and φ: G → Aut(ℤ) is a homomorphism, which are realizable in the way above and the homotopy types of all possible orbit spaces as well. Next, we consider the family of all groups which have virtual cohomological dimension one and which act on some Σ(2n). Those groups consist of free groups and semi-direct products F ⋊ ℤ2 with F a free group. For a group G from the family above and a homomorphism φ: G → Aut(ℤ), we present an algebraic criterion equivalent to the realizability of the pair (G, φ). It turns out that any realizable pair can be realized on some Σ(2n) with dim Σ(2n) ≤ 2n + 1.

Classification of Hermitian Forms. VI Group Rings

1976 ◽  
Vol 103 (1) ◽  
pp. 1 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Group Rings ◽  
Hermitian Forms

On the classification of Hermitian forms

1972 ◽  
Vol 18 (1-2) ◽  
pp. 119-141 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Hermitian Forms
Sign in / Sign up

Export Citation Format

Share Document