Cornered Heegaard Floer homology

Abstract

Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. We construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners, and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.

Updated to published version

References in corpus (5)

• Bimodules in bordered Heegaard Floer homology
• On the Classification of Topological Field Theories
• Bordered Floer homology for sutured manifolds
• Computing HF^ by factoring mapping classes
• Joining and gluing sutured Floer homology

Cited by in corpus (5)

• The Alexander module, Seifert forms, and categorification
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Compatibility in Ozsvath-Szabo's bordered HFK via higher representations
• On the decategorification of some higher actions in Heegaard Floer homology
• Strands algebras and the affine highest weight property for equivariant hypertoric categories