Journal title
Advances in Mathematics
DOI
10.1016/j.aim.2016.06.005
Volume
299
Last updated
2024-04-10T13:25:59.813+01:00
Page
940-1038
Abstract
It has been a central open problem in Heegaard Floer theory whether cobordisms of links induce homomorphisms on the associated link Floer homology groups. We provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds, and showing that such a cobordism induces a map on sutured Floer homology. This map is a common generalization of the hat version of the closed 3-manifold cobordism map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez, and Mati´c. We show that sutured Floer homology, together with the above cobordism maps, forms a type of TQFT in the sense of Atiyah. Applied to the sutured manifold cobordism complementary to a decorated link cobordism, our theory gives rise to the desired map on link Floer homology. Hence, link Floer homology is a categorification of the multi-variable Alexander polynomial. We outline an alternative definition of the contact gluing map using only the contact element and handle maps. Finally, we show that a Weinstein sutured manifold cobordism preserves the contact element.
Symplectic ID
627178
Submitted to ORA
On
Favourite
Off
Publication type
Journal Article
Publication date
01 Jan 2016