The Seiberg–Witten invariants and 4–manifolds with essential tori
نویسنده
چکیده
A formula is given for the Seiberg–Witten invariants of a 4–manifold that is cut along certain kinds of 3–dimensional tori. The formula involves a Seiberg– Witten invariant for each of the resulting pieces. AMS Classification numbers Primary: 57R57 Secondary: 57M25, 57N13
منابع مشابه
Hyperbolic Manifolds, Harmonic Forms, and Seiberg-Witten Invariants
New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on compact 4-manifolds of constant negative sectional curvature.
متن کاملIntersection theory of coassociative submanifolds in G2-manifolds and Seiberg-Witten invariants
We study the problem of counting instantons with coassociative boundary condition in (almost) G2-manifolds. This is analog to the open GromovWitten theory for counting holomorphic curves with Lagrangian boundary condition in Calabi-Yau manifolds. We explain its relationship with the Seiberg-Witten invariants for coassociative submanifolds. Intersection theory of Lagrangian submanifolds is an es...
متن کاملHiggs Bundles and Four Manifolds
It is known that the Seiberg-Witten invariants, derived from supersymmetric Yang-Mill theories in four-dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson-Witten and Vafa-Witten theories on a Kähler manifold based on Higgs Bundles. We showed, in particular, that the partition function of our generalized Vafa-Wit...
متن کاملSeiberg-Witten invariants of mapping tori, symplectic fixed points, and Lefschetz numbers
Let f : Σ → Σ be an orientation preserving diffeomorphism of a compact oriented Riemann surface. This paper relates the Seiberg-Witten invariants of the mapping torus Yf to the Lefschetz invariants of f .
متن کاملRefined Seiberg-witten Invariants
In the past two decades, gauge theoretic methods became indispensable when considering manifolds in dimension four. Initially, research centred around the moduli spaces of Yang-Mills instantons. Simon Donaldson had introduced the instanton equations into the field. Using cohomological data of the corresponding moduli spaces, he defined invariants which could effectively distinguish differentiab...
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 2001