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A note on mapping class group actions on derived categories


Author: Nicolò Sibilla
Journal: Proc. Amer. Math. Soc. 142 (2014), 1837-1848
MSC (2010): Primary 14F05; Secondary 53D37
DOI: https://doi.org/10.1090/S0002-9939-2014-11914-9
Published electronically: February 24, 2014
MathSciNet review: 3182005
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Abstract: Let $ X_n$ be a cycle of $ n$ projective lines and $ \mathbb{T}_n$ a symplectic torus with $ n$ punctures. Using the theory of spherical twists introduced by Seidel and Thomas, the author will define an action of the pure mapping class group of $ \mathbb{T}_n$ on $ D^b(Coh(X_n))$. The motivation comes from homological mirror symmetry for degenerate elliptic curves, which was studied by the author with Treumann and Zaslow.


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Additional Information

Nicolò Sibilla
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Address at time of publication: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Email: sibilla@mpim-bonn.mpg.de

DOI: https://doi.org/10.1090/S0002-9939-2014-11914-9
Received by editor(s): October 17, 2011
Received by editor(s) in revised form: May 8, 2012, and June 29, 2012
Published electronically: February 24, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.