Monopoles and Three-Manifolds

By P. Kronheimer, T. Mrowka. 2008

448 citations recorded by the source corpus.

Subfields: Demography, Genetics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/a4eb59458fce889e8f59ecbc887b696e292af4a6

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Citations in the corpus

The embedded contact homology index revisited (2008, background): “Recall from [16] that Seiberg-Witten Floer homology also has an absolute grading by homotopy classes of oriented 2-plane fields.”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “In particular, given a three-dimensional manifold Y , by studying the equations on R × Y , one can construct an invariant called the Seiberg-Witten Floer homology of Y [MW01, Man03, Frø10, KM07].”
Monopole Floer homology for rational homology 3-spheres (2008, background): “In particular, we do not see how to apply the unique continuation results of [13].”
Fivebranes and 3-manifold homology (2016, background): “2) should categorify SW invariants and give monopole Floer homology which is isomorphic [21] to the Heegaard Floer homology (and the corresponding version of the ECH theory, as in (1.”
Instanton Floer homology and the Alexander polynomial (2009, background): “Y / : (In the case of connected manifolds YC and Y , this formula reduces to the one that appears in [8] for the monopole case.”
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].”
A link surgery spectral sequence in monopole Floer homology (2009, methodology): “is compact for the appropriate topology (see [13], Section 26.”
Analytic Continuation Of Chern-Simons Theory (2010, methodology): “e relevant determinant line bundle. This amounts to a choice of relative orientations of the cycles C and Jσ that we are comparing. Such choices of sign and orientation are discussed in, for example, [46] in the context of ﬁnite-dimensional Morse theory and Floer cohomology. 69 t→ −∞ and AM → Aτ for”
BPS spectra and 3-manifold invariants (2017, background): “ogical invariants of 3-manifolds, is based on gauge theory. The famous examples are Donaldson-Witten and Seiberg-Witten (SW) invariants of 4- and 3-manifolds, and corresponding instanton and monopole [1] Floer homologies of 3-manifolds. All of them were extensively studied in mathematical literature”
Quantitative embedded contact homology (2010, methodology): “This follows from a much stronger theorem of Taubes [22, 23, 24, 25] asserting that there is a canonical isomorphism between embedded contact homology and a version of SeibergWitten Floer cohomology as defined by Kronheimer-Mrowka [14].”
Making cobordisms symplectic (2015, background): “ovided that it admits a symplectic embedding of a suciently large symplectic ball. The assumption that in the 3-dimensional case the positive boundary is overtwisted is essential. In particular, see [21, 15]: Proposition 1.7. Suppose (W;!;˘ ;˘ +) is an exact 4-dimensional symplectic cobordism and th”
Beyond ECH capacities (2014, methodology): “) It follows from a theorem of Taubes [24], identifying ECH with a version of Seiberg-Witten Floer cohomology [16], that ECH(Y, λ,Γ, J) depends only on Y , the contact structure(5) ξ = Ker(λ), and Γ.”
Sutures and contact homology I (2010, background): “1Both Seiberg–Witten Floer homology and ECH have absolute gradings by homotopy classes of oriented 2–plane fields on M (see [32; 25]), and it is natural to conjecture that Taubes’s isomorphism between them respects these gradings.”
Instanton Floer homology with Lagrangian boundary conditions (2006, methodology): “The method was also used by Donaldson–Kronheimer [11, pp150] and Taubes [31] to prove unique continuation results for anti-self-dual instantons and by Kronheimer–Mrowka [20] and in [27] for the Seiberg–Witten equations.”
Torsion contact forms in three dimensions have two or infinitely many Reeb orbits (2017, unknown): “By results of Kronheimer-Mrowka [23] on the nontriviality of the latter, it then follows that there are infinitely many(5) holomorphic curves in R ˆ Y counted by the U map on ECH.”