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Surgery exact triangles in involutive Heegaard Floer homology

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arxiv 2011.00113 v2 pith:E2CKUMM6 submitted 2020-10-30 math.GT

Kristen Hendricks , Jennifer Hom , Matthew Stoffregen , Ian Zemke This is my paper · ORCID
classification math.GT
keywords homologysurgeryexactinvolutivefloerformulagiveheegaard
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We establish a surgery exact triangle for involutive Heegaard Floer homology by using a doubling model of the involution. We use this exact triangle to give an involutive version of Ozsv\'ath-Szab\'o's mapping cone formula for knot surgery. As an application, we use this surgery formula to give examples of integer homology spheres that are not homology cobordant to any linear combination of Seifert fibered spaces.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Satellites and telescopes: a concordance formula for bordered Floer homology

    math.GT 2026-06 conditional novelty 7.0 of 10

    Locally symmetric endomorphisms of the knot Floer complex correspond, up to a canonical class theta^-_K, to type-D endomorphisms of the bordered complement, making satellite concordance maps combinatorially computable.

  2. The link surgery formula and equivariant surgeries

    math.GT 2025-07 conditional novelty 7.0 of 10

    An equivariant link surgery formula is proved, giving diffeomorphism-induced maps on Heegaard Floer homology, and used to show the kernel of the forgetful map from the equivariant homology cobordism group contains a Z...

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