# 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} }

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

#### 3 Citations

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#### References

SHOWING 1-7 OF 7 REFERENCES

Non–trivial harmonic spinors on generic algebraic surfaces

- Mathematics
- 1996

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 is… Expand

Elliptic Boundary Problems for Dirac Operators

- Mathematics
- 1993

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 about… Expand

A Course in Arithmetic

- Mathematics
- 1973

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 on… Expand

A characterization of the Z^n lattice

- Mathematics
- 1995

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 not… Expand

Monopoles and four-manifolds

- Mathematics, Physics
- 1994

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 defining… Expand

The orientation of Yang-Mills moduli spaces and 4-manifold topology

- Mathematics
- 1987

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 standard… Expand

The Genus of Embedded Surfaces in the Projective Plane

- Mathematics
- 1994

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 the… Expand