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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Homology of regular coverings of spun CW pairs with applications to knot theory


Author: W. L. Motter
Journal: Proc. Amer. Math. Soc. 58 (1976), 331-338
MSC: Primary 57C45
DOI: https://doi.org/10.1090/S0002-9939-1976-0407852-6
MathSciNet review: 0407852
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Abstract: The $ p$-spin of a pair of CW complexes, one a subcomplex of the other, is defined. The algebraic properties of certain tensor-product chain complexes are used to calculate the homology groups of regular coverings of such spun pairs where these groups are considered as modules over the integral group ring of the group of covering transformations. In §4, by using the free differential calculus and ``geometric presentations'' for fundamental groups, presentations for certain homology groups are developed. In §§5 and 6 these results are used to analyze the homology and associated invariants for coverings of complements of higher-dimensional knots and torus-like embeddings in the sphere obtained by $ p$-spinning.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0407852-6
Keywords: CW complexes, spun CW pairs, regular coverings, homology of product complexes, free differential calculus, presentations for homology groups, spun knots, polynomial invariants, fibered embeddings
Article copyright: © Copyright 1976 American Mathematical Society