On exotic Lagrangian tori in ℂℙ2

Vianna, Renato

doi:10.2140/gt.2014.18.2419

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On exotic Lagrangian tori in $\mathbb{CP}^2$

Renato Vianna

Geometry & Topology 18 (2014) 2419–2476

DOI: 10.2140/gt.2014.18.2419

Abstract

We construct an exotic monotone Lagrangian torus in ${ℂ ℙ}^{2}$ using techniques motivated by mirror symmetry. We show that it bounds $10$ families of Maslov index $2$ holomorphic discs, and it follows that this exotic torus is not Hamiltonian isotopic to the known Clifford and Chekanov tori.

Keywords

exotic Lagrangian, Clifford, Chekanov, torus, tori

Mathematical Subject Classification 2010

Primary: 53D12

Secondary: 53D37, 53D40

References

Publication

Received: 9 July 2013

Revised: 9 January 2014

Accepted: 11 February 2014

Published: 2 October 2014

Proposed: Yasha Eliashberg

Seconded: Leonid Polterovich, Simon Donaldson

Authors

Renato Vianna
Department of Mathematics University of California at Berkeley 1087 Evans Hall Berkeley, CA 94720-3840 USA
http://math.berkeley.edu/~renato

Volume 18, issue 4 (2014)