On the algebra of cornered Floer homology. (12th June 2013) - Douglas, Christopher L.; Manolescu, Ciprian
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 nil‐Coxeter 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 towards the structure of a potential Floer homology theory of 3‐manifolds with codimension‐2 corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.