Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

Non-abelian cohomology via parity quasi-complexes

Pages: 49 – 58

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a5


Lucian M. Ionescu (Department of Mathematics, Illinois State University, Normal, Il., U.S.A.)


The homotopy category of parity quasi-complexes is introduced. The homotopy structure is compatible with the non-abelian homology of parity quasi-complexes.

Parity contracting homotopies are defined, determining the parity free resolutions in a canonical way, enabling the nonabelian bar construction.

In this way, the even/odd grouping of the simplicial maps in the cocycle conditions of nonabelian cohomology is explained.

2010 Mathematics Subject Classification

Primary 18G10, 18G55, 57T30. Secondary 18G25.

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