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  Non-orientable link cobordisms and torsion order in Floer homologies

Gong, S., & Marengon, M. (2023). Non-orientable link cobordisms and torsion order in Floer homologies. Algebraic & Geometric Topology, 23(6), 2627-2672. doi:10.48550/arXiv.2010.06577.

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© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

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 Creators:
Gong, Sherry, Author
Marengon, Marco1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology
 Abstract: We use unoriented versions of instanton and knot Floer homology to prove inequalities involving the Euler characteristic and the number of local maxima appearing in unorientable cobordisms, which mirror results of a recent paper by Juhasz, Miller, and Zemke concerning orientable cobordisms. Most of the subtlety in our argument lies in the fact that maps for non-orientable cobordisms require more complicated decorations than their orientable counterparts. We introduce unoriented versions of the band unknotting number and the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. Finally, we show that the difference between the unoriented refined cobordism distance of a knot $K$ from the unknot and the non-orientable slice genus of $K$ can be arbitrarily large.

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Language(s): eng - English
 Dates: 2023
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 2010.06577
DOI: 10.48550/arXiv.2010.06577
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Title: Algebraic & Geometric Topology
Source Genre: Journal
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Publ. Info: Mathematical Sciences Publishers
Pages: - Volume / Issue: 23 (6) Sequence Number: - Start / End Page: 2627 - 2672 Identifier: -