Cohomology of Split Group Extensions and Characteristic Classes

Details Cohomology of Split Group Extensions and Characteristic Classes Cohomology of Split Group Extensions and Characteristic Classes

2007-07-24

arxiv.org/abs/0707.3526v2

Journal of Algebra, Volume 321, Issue 10, 15 May 2009, Pages 2916-2925

Mathematics

Algebraic Topology

13 pages

Scientific paper

There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in a given page of the spectral sequence provided the differentials in the previous pages are all zero. When L decomposes into a sum of G-sublattices, we show that there are defining relations between the characteristic classes of L and the characteristic classes of its summands.

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