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Double bubble plumbings and two-curve flops

Published version
Peer-reviewed

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Authors

Smith, Ivan 
Wemyss, Michael 

Abstract

jats:titleAbstract</jats:title>jats:pWe discuss the symplectic topology of the Stein manifolds obtained by plumbing two 3-dimensional spheres along a circle. These spaces are related, at a derived level and working in a characteristic determined by the specific geometry, to local threefolds which contain two floppable jats:inline-formulajats:alternativesjats:tex-math$$(-1,-1)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mo(</mml:mo> mml:mo-</mml:mo> mml:mn1</mml:mn> mml:mo,</mml:mo> mml:mo-</mml:mo> mml:mn1</mml:mn> mml:mo)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>-curves meeting at a point. Using contraction algebras we classify spherical objects on the B-side, and derive topological consequences including a complete description of the homology classes realised by graded exact Lagrangians. </jats:p>

Description

Acknowledgements: Jonny Evans initiated our study of the symplectic topology of double bubbles and made numerous influential suggestions. The authors are also grateful to Denis Auroux, Matt Booth, Ben Davison, Tobias Ekholm, Karin Erdmann, Yankı Lekili, Cheuk Yu Mak, Sibylle Schroll and Paul Seidel for helpful conversations. The authors thank the anonymous referee for their numerous detailed queries and comments.

Keywords

53D37, 14J33, 14J30, 16S38, 53D49

Journal Title

SELECTA MATHEMATICA-NEW SERIES

Conference Name

Journal ISSN

1022-1824
1420-9020

Volume Title

Publisher

Springer Science and Business Media LLC