On the algebra of cornered Floer homology

Christopher L. Douglas; Ciprian Manolescu

doi:10.1112/jtopol/jtt013

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arXiv · 1105.0113

On the algebra of cornered Floer homology

Christopher L. Douglas·Ciprian Manolescu

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Abstract

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.

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BibTeX RIS

Christopher L. Douglas, Ciprian Manolescu. 2011-04-30. On the algebra of cornered Floer homology. https://doi.org/10.1112/jtopol%2Fjtt013

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