Structural results in wrapped Floer theory

We prove results relating different partially wrapped Fukaya categories, including a Kunneth formula, a 'stop removal' result relating partially wrapped Fukaya categories relative to different stops, and a gluing formula for wrapped Fukaya categories. We also show that the partially wrapped Fukaya category of a Weinstein manifold relative a singular isotropic stop is generated by the cocores of the critical handles and the small Lagrangian disks linking the stop. The proofs are mainly geometric, and the key underlying Floer theoretic fact is an exact triangle in the Fukaya category associated to Lagrangian surgery along a short Reeb chord at infinity.

[1]  Sheel Ganatra,et al.  Covariantly functorial wrapped Floer theory on Liouville sectors , 2017, Publications mathématiques de l'IHÉS.

[2]  Zachary Sylvan On partially wrapped Fukaya categories , 2016, Journal of Topology.

[3]  P. Massot,et al.  Contactomorphism groups and Legendrian flexibility , 2018, 1803.07997.

[4]  A. Polishchuk,et al.  Auslander orders over nodal stacky curves and partially wrapped Fukaya categories , 2017, Journal of Topology.

[5]  Georgios Dimitroglou Rizell,et al.  Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors , 2017, 1712.09126.

[6]  M. Abouzaid Homological mirror symmetry without correction , 2017, Journal of the American Mathematical Society.

[7]  Yuan Gao Wrapped Floer cohomology and Lagrangian correspondences , 2017, 1703.04032.

[8]  Georgios Dimitroglou Rizell Legendrian ambient surgery and Legendrian contact homology , 2012, 1205.5544.

[9]  Heather Lee Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions , 2016, 1608.04473.

[10]  Ailsa Keating Homological mirror symmetry for hypersurface cusp singularities , 2015, Selecta Mathematica.

[11]  V. Lyubashenko A∞-MORPHISMS WITH SEVERAL ENTRIES , 2015 .

[12]  T. Ekholm,et al.  Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold , 2013, 1307.8436.

[13]  M. Abouzaid A cotangent fibre generates the Fukaya category , 2010, 1003.4449.

[14]  M. Kontsevich Symplectic geometry of homological algebra , 2009 .

[15]  Alberto Abbondandolo,et al.  Floer homology of cotangent bundles and the loop product , 2008, 0810.1995.

[16]  A. Oancea The Künneth formula in Floer homology for manifolds with restricted contact type boundary , 2004, math/0403376.

[17]  K. Cieliebak Handle attaching in symplectic homology and the Chord Conjecture , 2002 .

[18]  P. Seidel A long exact sequence for symplectic Floer cohomology , 2001, math/0105186.

[19]  A. Weinstein Contact surgery and symplectic handlebodies , 1991 .

[20]  Y. Eliashberg TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2 , 1990 .

[21]  R. Thomason Homotopy colimits in the category of small categories , 1979, Mathematical Proceedings of the Cambridge Philosophical Society.