The Pontrjagin Dual of 3-Dimensional Spin Bordism

2016/12/08 by Brumfiel, Greg, Morgan, John · 2 citations
#55N22 #57R90 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.02860

Abstract

For each space X we define an explicit group, G(X), functorially in X. This group is constructed from the groups of cochains on X. Furthermore, we construct an explicit functorial pairing with values in R/Z between the cochain representatives for elements of G(X) and maps of closed 3-dimensional spin manifolds to X. This pairing induces a pairing between G(X) and the 3-dimensional spin bordism group of X and identifies each with the Pontrjagin dual of the other.

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