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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 nonorientable cobordisms, which mirror results of a recent paper by Juhász, Miller and Zemke concerning orientable cobordisms. Most of the subtlety in our argument lies in the fact that maps for nonorientable 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 nonorientable slice genus of K can be arbitrarily large.
Gong, Sherry 1 ; Marengon, Marco 2
@article{10_2140_agt_2023_23_2627,
author = {Gong, Sherry and Marengon, Marco},
title = {Nonorientable link cobordisms and torsion order in {Floer} homologies},
journal = {Algebraic and Geometric Topology},
pages = {2627--2672},
publisher = {mathdoc},
volume = {23},
number = {6},
year = {2023},
doi = {10.2140/agt.2023.23.2627},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2627/}
}
TY - JOUR AU - Gong, Sherry AU - Marengon, Marco TI - Nonorientable link cobordisms and torsion order in Floer homologies JO - Algebraic and Geometric Topology PY - 2023 SP - 2627 EP - 2672 VL - 23 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2627/ DO - 10.2140/agt.2023.23.2627 ID - 10_2140_agt_2023_23_2627 ER -
%0 Journal Article %A Gong, Sherry %A Marengon, Marco %T Nonorientable link cobordisms and torsion order in Floer homologies %J Algebraic and Geometric Topology %D 2023 %P 2627-2672 %V 23 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2627/ %R 10.2140/agt.2023.23.2627 %F 10_2140_agt_2023_23_2627
Gong, Sherry; Marengon, Marco. Nonorientable link cobordisms and torsion order in Floer homologies. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2627-2672. doi: 10.2140/agt.2023.23.2627
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