Involutive Heegaard Floer homology

Kristen Hendricks, Ciprian Manolescu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Using the conjugation symmetry on Heegaard Floer complexes, we define a 3-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and dN, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heegaard Floer homology of large integral surgeries on knots. We give explicit calculations in the case of L-space knots and thin knots. In particular, we show that V 0 detects the nonsliceness of the figure-eight knot. Other applications include constraints on which large surgeries on alternating knots can be homology-cobordant to other large surgeries on alternating knots.

Original languageEnglish (US)
Pages (from-to)1211-1299
Number of pages89
JournalDuke Mathematical Journal
Volume166
Issue number7
DOIs
StatePublished - May 15 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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