Floer Homology Groups in Yang-Mills Theory

By Simon Donaldson, M. Furuta, D. Kotschick. 2002

309 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/38cbbd3212fe3112bf4ea7b71af3da9bf49636d9

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Citations in the corpus

Geometry and analysis of spin equations (2004, methodology): “Now we can get the estimate from [D], Lemma 3.”
On the Floer homology of plumbed three-manifolds (2002, background): “The resulting package has many properties of a topological quantum field theory, and moreover it is closely related to its gauge-theoretic counterparts, DonaldsonFloer (see [1]) and Seiberg-Witten theory (see [17], [9], [8]).”
Knots, sutures, and excision (2008, methodology): “done using either monopole Floer homology [18] or instanton Floer homology [4] in place of the Heegaard version.”
Monopole Floer homology for rational homology 3-spheres (2008, unknown): “we define, following [4], homomorphisms”
The Seiberg–Witten equations and the Weinstein conjecture (2006, background): “% M as a manifold with boundary, and Theorem 4.1 provides only another example of what is observed by Donaldson [D] in the context of SU(2) gauge theory: A construction that gives a numerical gauge theory invariant to a 4-manifold with no boundary generalizes to a manifold with boundary so as to giv”
A compactification of the moduli space of twisted holomorphic maps (2004, background): “something very general (see for example Chapter 3 in [D] for the case of instanton Floer homology).”
Floer Homology and the Heat Flow (2003, background): “An elegant proof of the Fredholm property for general p > 1 was given by Donaldson [3] for the instanton case; it adapts easily to the symplectic case [18].”
Localization for Involutions in Floer Cohomology (2010, background): “The whole of Section 2 is devoted to a detailed explanation of the Morse-theoretic construction, where we are careful to use only arguments which are readily transplanted into Floer theory.”
A stable cohomotopy refinement of Seiberg-Witten invariants: I (2002, background): “t C s = Mcis independent of L. It remains to gain control of the constants in the elliptic estimate. It is convenient to invoke the theory of elliptic operators for manifolds with tubular ends, as in [3]. To do so, we attach semi-inﬁnite tubes to both positive and negative parts of X = X− ∪X+, to ge”
Knot homology groups from instantons (2008, unknown): “C̄∗(Y#T3;K,Φ)δ := C∗(Y#T 3;K,Φ)δ / Z/N F̄ IN∗ (Y,K) := H(C̄∗(Y#T 3;K,Φ)δ)”
Quilted Floer cohomology (2009, methodology): “With these remarks in mind, we can follow the standard construction of Floer theory (which is currently probably best outlined in [29] for the case of holomorphic cylinders, fully executed in [5] for a gauge theoretic setting, and hopefully soon available in [24] for holomorphic strips).”