Equivariant CW-Complexes and the Orbit Category

Hambleton, Ian; Pamuk, Semra; Yalcin, Ergun

doi:10.48550/arxiv.0807.3357

Cited by 3 publications

(4 citation statements)

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“…], H ≤ G, admits a finite length projective resolution. This follows from the orbit category version of Rim's theorem (see [15,Theorem 3.8]). However, the adjunction formula [20, 17.21] shows that, for example, the module…”

Section: Dress Induction Over the Orbit Categorymentioning

confidence: 99%

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Equivariant CW-complexes and the orbit category

Hambleton¹,

Pamuk²,

Yalcin³

2013

Comment. Math. Helv.

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Section: Dress Induction Over the Orbit Categorymentioning

confidence: 99%

“…For each prime p, the homology modules H i (C) ⊗ Z p admit finite projective resolutions over Z p Γ G , so by [15,Prop. 3.11] the homology modules H i (C) admit finite projective resolutions over ZΓ G .…”

Section: Lemma 310 a Super Class Function ϕ Is A Mod P Resolving Func...mentioning

confidence: 99%

Equivariant CW-complexes and the orbit category

Hambleton¹,

Pamuk²,

Yalcin³

2013

Comment. Math. Helv.

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“…Proof. Since H 0 (C) = H 0 (D), this follows from the version of Schanuel's Lemma over the orbit category given in the proof of [4,Lemma 8.12]. By construction…”

Section: The Chain Complexmentioning

confidence: 91%

A remark about dihedral group actions on spheres

Hambleton

2010

Bulletin of the London Mathematical Society

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“…Note also that for constructions of group actions, algebraic models over the orbit category are more useful than chain complexes of permutation modules. For more details on the construction of group actions on homotopy spheres, see [4] and [11].…”

Section: Periodicity Of Relative Cohomologymentioning

confidence: 99%

Relative group cohomology and the orbit category

Pamuk¹,

Yalcin²

2012

Preprint

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Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F -projective resolution for Z when F is the family of all subgroups H ≤ G with rk H ≤ rk G − 1. We answer this question negatively by calculating the relative group cohomology F H * (G, F 2 ) where G = Z/2 × Z/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology F H * (G, M ) can be calculated using the ext-groups over the orbit category of G restricted to the family F . In second part of the paper, we discuss the construction of a spectral sequence that converges to the cohomology of a group G and whose horizontal line at E 2 page is isomorphic to the relative group cohomology of G.

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Equivariant CW-Complexes and the Orbit Category

Cited by 3 publications

References 0 publications

Equivariant CW-complexes and the orbit category

Equivariant CW-complexes and the orbit category

A remark about dihedral group actions on spheres

Relative group cohomology and the orbit category

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