A remark on the geography problem in Heegaard Floer homology

Jonathan Hanselman, Çağatay Kutluhan, Tye Lidman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced Floer homology. Up to absolute grading shifts, there are only two. We use this corollary to show that the chain complex depicted by Ozsváth, Stipsicz, and Szabó to argue that there is no algebraic obstruction to the existence of knots with trivial ɛ invariant and non-trivial Υ invariant cannot be realized as the knot Floer complex of a knot.

Original languageEnglish (US)
Title of host publicationBreadth in Contemporary Topology - Georgia International Topology Conference, 2017
EditorsDavid T. Gay, Weiwei Wu
PublisherAmerican Mathematical Society
Number of pages9
ISBN (Print)9781470442491
StatePublished - 2019
EventGeorgia International Topology Conference, 2017 - Athens, Georgia
Duration: May 22 2017Jun 2 2017

Publication series

NameProceedings of Symposia in Pure Mathematics
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X


ConferenceGeorgia International Topology Conference, 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


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