Cobordisms of sutured manifolds

András Juhász

Published 2009-10-22, updated 2015-04-05Version 3

We introduce a natural notion of cobordism between sutured manifolds. Then we construct a map on sutured Floer homology, induced by cobordisms between balanced sutured manifolds. This map is a common generalization of the hat version of the cobordism map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez, and Mati\'c. We show that SFH, together with the above cobordism maps, form a type of TQFT in the sense of Atiyah. As a special case, our theory gives rise to a map on link Floer homology, induced by decorated link cobordisms.