English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Non-orientable link cobordisms and torsion order in Floer homologies

MPS-Authors
/persons/resource/persons274094

Marengon,  Marco
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Gong, S., & Marengon, M. (in press). Non-orientable link cobordisms and torsion order in Floer homologies. Algebraic & Geometric Topology, To appear.


Cite as: https://hdl.handle.net/21.11116/0000-000A-7B88-3
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.