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

16 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

Access to Document

10.1515/crelle-2014-0064

Cite this

@article{93e1083f558440bfa30962cf1d4cc95f,

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.",

author = "Matthew Hedden and Levine, \{Adam Simon\}",

note = "Publisher Copyright: {\textcopyright} De Gruyter 2016.",

year = "2016",

month = nov,

doi = "10.1515/crelle-2014-0064",

language = "English (US)",

volume = "2016",

pages = "129--154",

journal = "Journal fur die Reine und Angewandte Mathematik",

issn = "0075-4102",

publisher = "Walter de Gruyter GmbH",

number = "720",

}

TY - JOUR

T1 - Splicing knot complements and bordered floer homology

AU - Hedden, Matthew

AU - Levine, Adam Simon

N1 - Publisher Copyright: © De Gruyter 2016.

PY - 2016/11

Y1 - 2016/11

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.

UR - https://www.scopus.com/pages/publications/85009913056

UR - https://www.scopus.com/inward/citedby.url?scp=85009913056&partnerID=8YFLogxK

U2 - 10.1515/crelle-2014-0064

DO - 10.1515/crelle-2014-0064

M3 - Article

AN - SCOPUS:85009913056

SN - 0075-4102

VL - 2016

SP - 129

EP - 154

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 720

ER -

Splicing knot complements and bordered floer homology

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this