Cobordisms of sutured manifolds

Details Cobordisms of sutured manifolds Cobordisms of sutured manifolds

2009-10-22

arxiv.org/abs/0910.4382v2

Mathematics

Geometric Topology

53 pages, 11 figures, added a section on Weinstein cobordisms, improved exposition

Scientific paper

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 recently defined by Honda, Kazez, and Matic. 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.

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