Corpus ID: 55036727

A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms

@article{Katz2012APV,
  title={A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms},
  author={Mikhail G. Katz},
  journal={arXiv: Differential Geometry},
  year={2012}
}
  • M. Katz
  • Published 2012
  • Mathematics, Physics
  • arXiv: Differential Geometry
A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms. 
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References

SHOWING 1-7 OF 7 REFERENCES
Non–trivial harmonic spinors on generic algebraic surfaces
We disprove Hitchin's conjecture to the effect that for a generic complex structure on a simply connected spin complex surface the square root of the canonical bundle has no more cohomology then isExpand
Elliptic Boundary Problems for Dirac Operators
The major goal of this book is to make the theory of elliptic boundary problems accessible to mathematicians and physicists working in global analysis and operator algebras. The book is aboutExpand
A Course in Arithmetic
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem onExpand
A characterization of the Z^n lattice
We use theta series and modular forms to prove that Z^n is the only integral unimodular lattice of rank n without characteristic vectors of norm <n, i.e. the only integral unimodular lattice notExpand
Monopoles and four-manifolds
Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of definingExpand
The orientation of Yang-Mills moduli spaces and 4-manifold topology
Si X est une 4-variete lisse orientee fermee dont la forme intersection Q:H 2 (X; Z)/Torsion→Z est definie negative, alors la forme est equivalente sur les entiers a la forme standardExpand
The Genus of Embedded Surfaces in the Projective Plane
1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of theExpand