Equivariant Seiberg-Witten Floer Homology
نویسندگان
چکیده
3 Morse-Bott theory 30 3.1 Framed moduli space . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Gradient flow lines . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Relative Morse Index . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 Decay estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Transversality of M(Oa, Ob) . . . . . . . . . . . . . . . . . . . . . 42
منابع مشابه
Variants of Equivariant Seiberg-Witten Floer Homology
For a rational homology 3-sphere Y with a Spin structure s, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology in [5] lead to a collection of variants HF ∗,U(1)(Y, s), HF SW,∞ ∗,U(1) (Y, s) HF SW,+ ∗,U(1)(Y, s), ĤF SW ∗ (Y, s) and HF SW red,∗(Y, s) which are topological invariants. We establish a long exact sequence relating HF ∗,U(1)(Y,...
متن کاملSeiberg – Witten – Floer stable homotopy type of three - manifolds with b 1 = 0
Using Furuta’s idea of finite dimensional approximation in Seiberg–Witten theory, we refine Seiberg–Witten Floer homology to obtain an invariant of homology 3–spheres which lives in the S1–equivariant graded suspension category. In particular, this gives a construction of Seiberg–Witten Floer homology that avoids the delicate transversality problems in the standard approach. We also define a re...
متن کاملSe p 20 03 SEIBERG - WITTEN - FLOER STABLE HOMOTOPY TYPE OF THREE - MANIFOLDS WITH b 1 = 0
Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S 1-equivariant graded suspension category. In particular, this gives a construction of Seiberg-Witten Floer homology that avoids the delicate transversal-ity problems in the standard approach. We also define a ...
متن کامل00 1 SEIBERG - WITTEN - FLOER STABLE HOMOTOPY TYPE OF THREE - MANIFOLDS WITH b 1 = 0
Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten-Floer homology to obtain an invariant of homology 3-spheres which lives in the S 1-equivariant graded suspension category. We also define a relative invariant of four-manifolds with boundary and use it to give new proofs to some results of Frøyshov from [Fr].
متن کاملFloer Theory and Its Topological Applications
We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and four-manifolds with boundary. We then describe Floer stable homotopy types, the related Pin(2)-equivariant Seiberg-Witten Floer homology, and its application to the triangulation conjecture.
متن کاملPin(2)-equivariant Seiberg-witten Floer Homology and the Triangulation Conjecture
We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Frøyshov’s correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that there are no homology 3-spheres Y of Rokhlin invariant one such that Y #Y bounds a...
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تاریخ انتشار 1996