Contact structures, sutured Floer homology and TQFT

By K. Honda, W. Kazez, G. Matić. 2008

82 citations recorded by the source corpus.

We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',\Gamma') into a larger sutured manifold (M,\Gamma), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its properties.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Neurology

View Paper: https://www.semanticscholar.org/paper/2d7944f84a9410dba529e17bc38eecddecda4ce5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Neurology

Citations in the corpus

The contact invariant in sutured Floer homology (2007, background): “Further properties of the contact invariant will be discussed in the sequel [ 16 ].”
Bordered Floer homology for sutured manifolds (2009, methodology): “To any arc diagram Z— or alternatively decorated sutured surface parametrized by Z—we associate a differential graded algebra A(Z), which is a subalgebra of some strand algebra, as defined in [8].”
Link cobordisms and functoriality in link Floer homology (2016, methodology): “natively, they can be dened in the hat avor of link Floer homology using the construction in [Juh15a], though this approach is somewhat dierent than the others in that it requires the gluing map in [HKM08] dened using contact geometry. In this section we construct maps associated to bands on CFL, an”
Khovanov homology detects the trefoils (2018, unknown): “Γi obtained by removing a standard neighborhood of K± i from Y. These contact manifolds are related to one another via positive and negative bypass attachments. By work of Honda, Kazez, and Mati´c in [HKM08], these bypass attachments induce maps on sutured Floer homology, ψ± i : SFH(−Y(K),−Γi) → SFH”
Link cobordisms and absolute gradings in link Floer homology (2017, methodology): “the hat avor of link Floer homology, for decorated link cobordisms in the above sense. The construction used the contact gluing map LINK COBORDISMS AND ABSOLUTE GRADINGS ON LINK FLOER HOMOLOGY 5 from [HKM08] as well as handle attachment maps similar to the ones from [OS06]. To such a decorated link ”
Cobordisms of sutured manifolds and the functoriality of link Floer homology (2009, background): “ OF SUTURED MANIFOLDS 63 Figure 11. A balanced cobordism W having no isolated components on the left, and the corresponding special cobordism W1 on the right. Remark 9.14. In the remark on page 11 of [14], a construction is outlined for a map from SFH(−M′,−γ′) to SFH(−M,−γ) that depends on a Spinc s”
A survey of Heegaard Floer homology (2013, background): “generated by OP. This theorem has several generalizations, which provide alternative proofs to the original statement. One is a gluing formula for convex decomposition due to Honda, Kazez, and Mati´c [30]. Given a convex decomposition pM,γq ù pM1,γ1q, they deﬁne a gluing map SFHpM1,γ1q Ñ SFHpM,γq, a”
A hierarchy of local symplectic filling obstructions for contact $3$-manifolds (2010, result): “ion is fully separating. This would be a direct generalization of [GHVHM,GH]. Some partial results in this direction are proved in the recent paper by Patrick Massot [Mas]; see also Honda-Kazez-Matic [HKM] and Mathews [Mat]. As we sketched in the above discussion of related results in [LW], the hier”