Splicing knot complements and bordered floer homology

Matthew Hedden; Adam Simon Levine

doi:10.1515/crelle-2014-0064

Splicing knot complements and bordered floer homology

Matthew Hedden, Adam Simon Levine

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.

Original language	English (US)
Pages (from-to)	129-154
Number of pages	26
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2016
Issue number	720
DOIs	https://doi.org/10.1515/crelle-2014-0064
State	Published - Nov 2016

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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title = "Splicing knot complements and bordered floer homology",

abstract = "We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.",

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AU - Levine, Adam Simon

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N2 - We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.

AB - We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.

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SN - 0075-4102

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ER -

Splicing knot complements and bordered floer homology

Abstract

All Science Journal Classification (ASJC) codes

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