Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 7 (2017), 1211-1299.
Involutive Heegaard Floer homology
Using the conjugation symmetry on Heegaard Floer complexes, we define a -manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to -equivariant Seiberg–Witten Floer homology. Further, we obtain two new invariants of homology cobordism, and , and two invariants of smooth knot concordance, and . 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 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.
Duke Math. J., Volume 166, Number 7 (2017), 1211-1299.
Received: 24 November 2015
Revised: 12 July 2016
First available in Project Euclid: 11 January 2017
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Hendricks, Kristen; Manolescu, Ciprian. Involutive Heegaard Floer homology. Duke Math. J. 166 (2017), no. 7, 1211--1299. doi:10.1215/00127094-3793141. https://projecteuclid.org/euclid.dmj/1484103841