On the algebra of cornered Floer homology. (12th June 2013)

• Record Type: Journal Article
• Authors: Douglas, Christopher L.; Manolescu, Ciprian
• Is Part Of: Journal of topology. Volume 7:Part 1(2014)
• Page Start: 1
• Page End: 68
• Publication Date: 2013-06-12
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/jtopol/jtt013
• Languages: English
• ISSNs: 1753-8416

Abstract

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.