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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


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Volume 2016, Issue 720

Issues

Splicing knot complements and bordered Floer homology

Matthew Hedden
  • Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, United States of America
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/ Adam Simon Levine
  • Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, United States of America
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Published Online: 2014-11-08 | DOI: https://doi.org/10.1515/crelle-2014-0064

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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About the article

Received: 2013-09-04

Revised: 2014-09-08

Published Online: 2014-11-08

Published in Print: 2016-11-01


Funding Source: National Science Foundation

Award identifier / Grant number: DMS-0906258

Award identifier / Grant number: DMS-1150872

Award identifier / Grant number: DMS-1004622

Matthew Hedden gratefully acknowledges support from NSF grant DMS-0906258, NSF CAREER grant DMS-1150872, and an Alfred P. Sloan Research Fellowship. Adam Simon Levine was partially supported by NSF Postdoctoral Research Fellowship grant DMS-1004622.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 720, Pages 129–154, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0064.

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