Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map

Mark Robert Leonard McLean

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E 1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms.
Original languageEnglish
Pages (from-to)473-512
Number of pages39
JournalSelecta Mathematica
Volume18
Issue number3
DOIs
Publication statusPublished - Sep 2012

Fingerprint

Lefschetz Fibration
Floer Homology
Spectral Sequence
homology
Monodromy
Iterate
Homology
Fixed point

Keywords

  • symplectic homology
  • Lefschetz fibrations
  • Floer homology
  • mondronomy map
  • primary 53D40
  • secondary 53D35
  • 37J10

Cite this

Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map. / McLean, Mark Robert Leonard.

In: Selecta Mathematica, Vol. 18, No. 3, 09.2012, p. 473-512 .

Research output: Contribution to journalArticle

McLean, Mark Robert Leonard. / Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map. In: Selecta Mathematica. 2012 ; Vol. 18, No. 3. pp. 473-512 .
@article{c17f3dbc70334b9b8a0a71b46388721e,
title = "Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map",
abstract = "We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E 1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms.",
keywords = "symplectic homology, Lefschetz fibrations, Floer homology, mondronomy map, primary 53D40, secondary 53D35, 37J10",
author = "McLean, {Mark Robert Leonard}",
year = "2012",
month = "9",
doi = "10.1007/s00029-011-0079-6",
language = "English",
volume = "18",
pages = "473--512",
journal = "Selecta Mathematica",
issn = "1022-1824",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

TY - JOUR

T1 - Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map

AU - McLean, Mark Robert Leonard

PY - 2012/9

Y1 - 2012/9

N2 - We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E 1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms.

AB - We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E 1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms.

KW - symplectic homology

KW - Lefschetz fibrations

KW - Floer homology

KW - mondronomy map

KW - primary 53D40

KW - secondary 53D35

KW - 37J10

U2 - 10.1007/s00029-011-0079-6

DO - 10.1007/s00029-011-0079-6

M3 - Article

VL - 18

SP - 473

EP - 512

JO - Selecta Mathematica

JF - Selecta Mathematica

SN - 1022-1824

IS - 3

ER -