Embedded contact homology and Seiberg–Witten Floer cohomology II

By Clifford H. Taubes. 2008

181 citations recorded by the source corpus.

This is a sequel to four earlier papers by the author that construct an isomorphism between the embedded contact homology and Seiberg‐Witten Floer cohomology of a compact 3‐manifold with a given contact 1‐form. These respective homology/cohomology theories carry additional structure; this sequel proves that the isomorphism that is constructed in the first four papers is compatible with this extra structure.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ce35e067f6477c74a57fd1727b1a216b24212ca

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In Mathematical Physics

Citations in the corpus

The embedded contact homology index revisited (2008, unknown): “The essential importance of the work of Cliff Taubes for this project should be self-evident.”
Proof of the Arnold chord conjecture in three dimensions, II (2010, unknown): “This follows from a much stronger theorem of the second author [15, 16, 17, 18] asserting that ECH is isomorphic to a version of Seiberg-Witten Floer cohomology as defined by KronheimerMrowka.”
Taubes’s proof of the Weinstein conjecture in dimension three (2009, result): “This follows from a much stronger result recently proved by Taubes [66, 67], which is the analogue of Gr=SW in this setting:”
Torsion contact forms in three dimensions have two or infinitely many Reeb orbits (2017, unknown): “It was shown by Taubes [26] that there is a canonical isomorphism between ECH and a version of Seiberg–Witten Floer cohomology, which identiﬁes the U –map on ECH with a corresponding “ U –map” on Seiberg–Witten Floer cohomology.”
The asymptotics of ECH capacities (2012, background): “Taubes [15] proved that if Y is connected, then there is a canonical isomorphism of relatively graded Z/2-modules”
A combinatorial spanning tree model for knot Floer homology (2011, background): “It is known (or soon will be) that monopole knot homology agrees with knot Floer homology, as a result of nearly one thousand pages of work of Taubes [50, 51, 52, 53, 54], Kutluhan–Lee–Taubes [20, 21, 22, 23, 24] and Colin–Ghiggini–Honda [6, 7], combined with work of Lekili [25].”
Connected sums and involutive knot Floer homology (2017, methodology): “In a different direction, due to the work of Taubes [35], Kutluhan, Lee and Taubes [14– 18], and Colin, Ghiggini and Honda [2–5] there are isomorphisms between certain versions of Heegaard Floer homology and the monopole Floer homology groups developed by Kronheimer and Mrowka [13].”
Symplectic embeddings into four‐dimensional concave toric domains (2013, unknown): “Taubes [15] proved that the embedded contact homology of a contact three-manifold is isomorphic to a version of its Seiberg–Witten Floer cohomology as defined by Kronheimer–Mrowka [11].”