Poincaré complex diagonals and the Bass trace conjecture

For a finitely dominated Poincaré duality space $M$ , we show how the first author's total obstruction $\mu _M$ to the existence of a Poincaré embedding of the diagonal map $M \to M \times M$ in [17] relates to the Reidemeister trace of the identity map of $M$ . We then apply this relationship...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics pp. 1 - 22
Main Authors Klein, John R., Naef, Florian
Format Journal Article
LanguageEnglish
Published United States Cambridge University Press 28.07.2023
Subjects
Bass trace conjecture
Mathematics
Poincaré duality space
Poincaré embedding
Reidemeister trace
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Summary:For a finitely dominated Poincaré duality space $M$ , we show how the first author's total obstruction $\mu _M$ to the existence of a Poincaré embedding of the diagonal map $M \to M \times M$ in [17] relates to the Reidemeister trace of the identity map of $M$ . We then apply this relationship to show that $\mu _M$ vanishes when suitable conditions on the fundamental group of $M$ are satisfied.
Bibliography:SC0022134
USDOE Office of Science (SC)
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2023.65