Application of group cohomology to space constructions

Authors:
Paul Igodt and Kyung Bai Lee

Journal:
Trans. Amer. Math. Soc. **304** (1987), 69-82

MSC:
Primary 57S30; Secondary 20J10

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906806-2

MathSciNet review:
906806

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Abstract: From a short exact sequence of crossed modules and a -cocycle , a -term cohomology exact sequence is obtained. Here the first and the last term are the ordinary (=abelian) cohomology groups, and is the center of the crossed module . The second term is shown to be in one-to-one correspondence with certain geometric constructions, called Seifert fiber space construction. Therefore, it follows that, if both the end terms vanish, the geometric construction exists and is unique.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906806-2

Keywords:
Nonabelian group cohomology,
Seifert fiber spaces,
infranil-manifolds

Article copyright:
© Copyright 1987
American Mathematical Society