Transfer Theory and Homology

Cheng, Yu

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Transfer Theory and Homology

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In this thesis, we develop three interpretations of the transfer homomorphism: via topological spaces, simplicial homology, and group theory. Historically, the first appearance was in group theory, from the permutation action of G on cosets of a subgroup. The constructions in topology and homological algebra can be interpreted this way through results on the fundamental groups and homology groups of covering spaces. The goal of this thesis is to describe enough background in each area to define and interpret the transfer homomorphism and to give some applications of the transfer in finite group theory.

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