SL(2,C) Floer Cohomology for Surgeries on Some Knots

Ikshu Neithalath

doi:10.1307/mmj/20216036

SL(2,C) Floer Cohomology for Surgeries on Some Knots

Ikshu Neithalath^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We establish a relationship between HP(Y ), the Abouzaid- Manolescu sheaf-theoretic SL(2,C) Floer cohomology for a surgery Y on a small knot in S³and Curtis' SL(2,C) Casson invariant. We use this to compute HP for most surgeries on two-bridge knots. We also compute HP for surgeries on two nonsmall knots, the granny and square knots.

Original language	English
Journal	Michigan Mathematical Journal
Volume	73
Issue number	5
Pages (from-to)	925-950
Number of pages	26
ISSN	0026-2285
DOIs	https://doi.org/10.1307/mmj/20216036
Publication status	Published - Nov 2023

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10.1307/mmj/20216036

https://arxiv.org/pdf/2002.04103

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title = "SL(2,C) Floer Cohomology for Surgeries on Some Knots",

abstract = "We establish a relationship between HP(Y ), the Abouzaid- Manolescu sheaf-theoretic SL(2,C) Floer cohomology for a surgery Y on a small knot in S3and Curtis' SL(2,C) Casson invariant. We use this to compute HP for most surgeries on two-bridge knots. We also compute HP for surgeries on two nonsmall knots, the granny and square knots.",

author = "Ikshu Neithalath",

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AB - We establish a relationship between HP(Y ), the Abouzaid- Manolescu sheaf-theoretic SL(2,C) Floer cohomology for a surgery Y on a small knot in S3and Curtis' SL(2,C) Casson invariant. We use this to compute HP for most surgeries on two-bridge knots. We also compute HP for surgeries on two nonsmall knots, the granny and square knots.

U2 - 10.1307/mmj/20216036

DO - 10.1307/mmj/20216036

M3 - Journal article

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JO - Michigan Mathematical Journal

JF - Michigan Mathematical Journal

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SL(2,C) Floer Cohomology for Surgeries on Some Knots

Abstract

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