Floer homology and fractional Dehn twists

Matthew Hedden, Thomas E. Mark

Research output: Research - peer-reviewArticle

Abstract

We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of the fractional Dehn twist coefficient of the monodromy of any of its open book decompositions with connected binding. We prove this by showing that the rank of Floer homology gives bounds for the number of boundary parallel right or left Dehn twists necessary to add to a surface automorphism to guarantee that the associated contact manifold is tight or overtwisted, respectively. By examining branched double covers, we also show that the rank of the Khovanov homology of a link bounds the fractional Dehn twist coefficient of its odd-stranded braid representatives.

LanguageEnglish (US)
Pages1-39
Number of pages39
JournalAdvances in Mathematics
Volume324
DOIs
StatePublished - Jan 14 2018

Profile

Dehn Twist
Floer Homology
Fractional
Coefficient
Heegaard Floer Homology
Open Book Decomposition
Khovanov Homology
Contact Manifold
Braid
Monodromy
Absolute value
Automorphism
Automorphisms
Odd
Cover
Necessary
Relationships

Keywords

  • 3-Manifold
  • Contact structure
  • Floer homology
  • Heegaard
  • Knot
  • L-space
  • Mapping class
  • Ractional Dehn twist

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Floer homology and fractional Dehn twists. / Hedden, Matthew; Mark, Thomas E.

In: Advances in Mathematics, Vol. 324, 14.01.2018, p. 1-39.

Research output: Research - peer-reviewArticle

Hedden, Matthew ; Mark, Thomas E./ Floer homology and fractional Dehn twists. In: Advances in Mathematics. 2018 ; Vol. 324. pp. 1-39
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