Cobordisms of sutured manifolds and the functoriality of link Floer homology
By Andr'as Juh'asz. 2009
78 citations recorded by the source corpus.
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 Matic. 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.
Subfields: Geometry and Topology, Mathematical Physics, Neurology
View Paper: https://www.semanticscholar.org/paper/d65bbb3803f0a00ac4f9f5004d346d02042550b0
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Citations in the corpus
- Link cobordisms and absolute gradings in link Floer homology (2017, methodology): “ong the arc A(i.e. removing two balls and computing the map induced by the knot cobordism from (S3;U) to (S3;U)). 1.5. Further remarks. In [JM16b] Juhasz and Marengon compute the cobordism maps from [Juh16] on \HFL associated to link cobordisms in S3 [0;1] and in doing so, compute the grading change”
- Link cobordisms and functoriality in link Floer homology (2016, methodology): “n such a case, the colorings become irrelevant, and our denition of a decorated LINK COBORDISMS AND FUNCTORIALITY IN LINK FLOER HOMOLOGY 7 link cobordism becomes essentially equivalent to the one in [Juh15a]. To this end, we make the following conjecture: Conjecture 1.3. The maps Fb W;F = P s2Spinc(”
- Quasi-stabilization and basepoint moving maps in link Floer homology (2016, methodology): “w;z t into the framework of a \graph TQFT" for surfaces embedded in four-manifolds with some extra decoration, similar to the TQFT for \HFL constructed using sutured Floer homology by Juhasz in [Juh15] and considered further in [JM15] for concordances. Such a TQFT construction for CFL1 UV will ”
- Connected sums and involutive knot Floer homology (2017, methodology): “Firstly, we prove Theorem 1.3, conjugation invariance for the link Floer TQFT.”