Instanton floer homology for two-component links

Eric Harper, Nikolai Saveliev

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For any oriented link of two components in an integral homology 3-sphere, we define an instanton Floer homology whose Euler characteristic is twice the linking number between the components of the link. We show that, for two-component links in the 3-sphere, this Floer homology does not vanish unless the link is split. We also relate our Floer homology to the KronheimerMrowka instanton Floer homology for links.

Original languageEnglish (US)
Article number1250054
JournalJournal of Knot Theory and its Ramifications
Volume21
Issue number5
DOIs
StatePublished - May 2012

Fingerprint

Floer Homology
Instantons
Linking number
Euler Characteristic
Homology
Vanish

Keywords

  • Floer homology
  • instanton
  • Knot
  • link
  • linking number

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Instanton floer homology for two-component links. / Harper, Eric; Saveliev, Nikolai.

In: Journal of Knot Theory and its Ramifications, Vol. 21, No. 5, 1250054, 05.2012.

Research output: Contribution to journalArticle

@article{b13d35d8d5cf42599fd19b3e872a387a,
title = "Instanton floer homology for two-component links",
abstract = "For any oriented link of two components in an integral homology 3-sphere, we define an instanton Floer homology whose Euler characteristic is twice the linking number between the components of the link. We show that, for two-component links in the 3-sphere, this Floer homology does not vanish unless the link is split. We also relate our Floer homology to the KronheimerMrowka instanton Floer homology for links.",
keywords = "Floer homology, instanton, Knot, link, linking number",
author = "Eric Harper and Nikolai Saveliev",
year = "2012",
month = "5",
doi = "10.1142/S0218216511010085",
language = "English (US)",
volume = "21",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",

}

TY - JOUR

T1 - Instanton floer homology for two-component links

AU - Harper, Eric

AU - Saveliev, Nikolai

PY - 2012/5

Y1 - 2012/5

N2 - For any oriented link of two components in an integral homology 3-sphere, we define an instanton Floer homology whose Euler characteristic is twice the linking number between the components of the link. We show that, for two-component links in the 3-sphere, this Floer homology does not vanish unless the link is split. We also relate our Floer homology to the KronheimerMrowka instanton Floer homology for links.

AB - For any oriented link of two components in an integral homology 3-sphere, we define an instanton Floer homology whose Euler characteristic is twice the linking number between the components of the link. We show that, for two-component links in the 3-sphere, this Floer homology does not vanish unless the link is split. We also relate our Floer homology to the KronheimerMrowka instanton Floer homology for links.

KW - Floer homology

KW - instanton

KW - Knot

KW - link

KW - linking number

UR - http://www.scopus.com/inward/record.url?scp=84858173639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858173639&partnerID=8YFLogxK

U2 - 10.1142/S0218216511010085

DO - 10.1142/S0218216511010085

M3 - Article

AN - SCOPUS:84858173639

VL - 21

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 5

M1 - 1250054

ER -