Seiberg-Witten-Floer Theory for Homology 3-Spheres
نویسنده
چکیده
We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relative Seiberg-Witten invariants are applied to certain homology spheres bounding Stein surfaces.
منابع مشابه
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 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 کاملA Monopole Homology for Integral Homology 3-spheres
To an integral homology 3-sphere Y , we assign a well-defined Z-graded (monopole) homology MH∗(Y, Iη(Θ; η0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow Iη(Θ; η0), where Θ is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and η0 is a reference perturbation datum. The definition uses the moduli space of ...
متن کاملOn the Intersection Forms of Spin Four-manifolds with Boundary
We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory. In the process we introduce the notion of a Floer KG-split homology sphere; this concept may be useful in an approach to the 11/8 conjecture.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008