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Dehn twist exact sequences through Lagrangian cobordism

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  05 November 2018

Cheuk Yu Mak  and
Weiwei Wu
Cheuk Yu Mak
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, CB3 0WB, UK email cym22@dpmms.cam.ac.uk
Weiwei Wu
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30606, USA email weiwei@math.uga.edu
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Abstract

This paper introduces a new Lagrangian surgery construction that generalizes Lalonde–Sikorav and Polterovich’s well-known construction, and combines this with Biran and Cornea’s Lagrangian cobordism formalism. With these techniques, we build a framework which both recovers several known long exact sequences (Seidel’s exact sequence, including the fixed point version and Wehrheim and Woodward’s family version) in symplectic geometry in a uniform way, and yields a partial answer to a long-term open conjecture due to Huybrechts and Thomas; this also involved a new observation which relates projective twists with surgeries.

Keywords

Lagrangian cobordismLagrangian surgeryDehn twistsprojective twists

MSC classification

Primary: 53D12: Lagrangian submanifolds; Maslov index 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category

Information

Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 12 , December 2018 , pp. 2485 - 2533
Copyright
© The Authors 2018 

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Footnotes

C.Y.M. is supported by NSF-grant DMS 1065927. W.W. is partially supported by CRM-ISM postdoctoral fellowship.

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