Compatible actions and cohomology of crystallographic groups.

DOI10.1016/j.jalgebra.2008.02.012zbMath1163.20032arXiv0704.1823OpenAlexW2037008300MaRDI QIDQ947528

Nansen Petrosyan, Jian Quan Ge, Adem, Alejandro, Pan, Jian Zhong

Publication date: 6 October 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1823

zbMATH Keywords

spectral sequencesgroup cohomologycrystallographic groupsflat manifoldsgerbes

Mathematics Subject Classification ID

Cohomology of groups (20J06) Homological methods in group theory (20J05) Equivariant homology and cohomology in algebraic topology (55N91) Other geometric groups, including crystallographic groups (20H15) Serre spectral sequences (55T10)

Related Items (12)

DDVV-type inequality for Hermitian matrices ⋮ TOPOLOGICAL K-THEORY OF THE GROUP C*-ALGEBRA OF A SEMI-DIRECT PRODUCT ℤⁿ ⋊ ℤ/m FOR A FREE CONJUGATION ACTION ⋮ Cohomology of split group extensions and characteristic classes. ⋮ The topological K-theory of certain crystallographic groups ⋮ On cohomology of crystallographic groups with cyclic holonomy of split type. ⋮ On the group cohomology of the semi-direct product \(\mathbb Z^n\rtimes_\rho\mathbb Z/m\) and a conjecture of Adem-Ge-Pan-Petrosyan. ⋮ SOME CONSIDERATIONS ON THE NONABELIAN TENSOR SQUARE OF CRYSTALLOGRAPHIC GROUPS ⋮ Twists on the torus equivariant under the 2-dimensional crystallographic point groups ⋮ Generators of Bieberbach groups with 2-generated holonomy group ⋮ Stable splittings, spaces of representations and almost commuting elements in Lie groups ⋮ Lieb-Schultz-Mattis theorem and the filling constraint ⋮ Cohomology of toroidal orbifold quotients

Cites Work

• Triples, fluxes, and strings
• Bieberbach groups and flat manifolds
• A counterexample to a conjecture of Steenrod
• Free resolutions for semi-direct products
• Comment on the generation number in orbifold compactifications
• On orbifolds with discrete torsion
• Cohomology of semidirect product groups
• Z/pZ Actions on (S n ) k
• Compact Flat Riemannian Manifolds II: The Cohomology of Z p -Manifolds
• Toroidal orbifolds, gerbes and group cohomology
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