On the invariance of the string topology coproduct

Nathalie Wahl

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arXiv · 1908.03857

On the invariance of the string topology coproduct

Nathalie Wahl

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Abstract

We give a variant of Naef's formula for the failure of invariance of the string topology coproduct under homotopy equivalences, using an obstruction class built from homotopy data associated to a homotopy equivalence as well as the ``fake diagonal''. The vanishing of our obstruction class can be seen as a way to measure a form of boundedness for homotopy equivalences. We show that the same obstruction rules the failure of invariance for a generalization of the coproduct to higher dimensional loops.

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BibTeX RIS

Nathalie Wahl. 2019-08-11. On the invariance of the string topology coproduct. https://arxiv.org/abs/1908.03857

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