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On the algebra of cornered Floer homology

By Christopher L. Douglas and Ciprian Manolescu


Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.Comment: a few minor revision

Topics: Mathematics - Geometric Topology, Mathematics - Algebraic Topology, Mathematics - Quantum Algebra, Mathematics - Symplectic Geometry, 57R56 (Primary) 57R58 (Secondary)
Year: 2013
DOI identifier: 10.1112/jtopol/jtt013
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