An application of gauge theory to four-dimensional topology

Simon Donaldson

doi:10.4310/jdg/1214437665

January 1, 1983Journal of Differential GeometryOpen Access

An application of gauge theory to four-dimensional topology

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Key Points

Determine the algebraic structure of the intersection form on compact, simply connected, oriented smooth 4-manifolds with positive-definite intersection forms.
Applied techniques from gauge theory and differential geometry to study smooth 4-manifold topology.
Analyzed the integral intersection form Q of compact, simply connected, oriented 4-manifolds.
Demonstrated that any positive-definite intersection form on a smooth, compact, simply connected 4-manifold is equivalent over the integers to the standard diagonal form.
Showed that relative to an appropriate basis, the intersection form decomposes as Q(u_1, u_2, ..., u_n) = u_1^2 + u_2^2 + ... + u_n^2.

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Implication

Theoretical analysis demonstrates that positive-definite intersection forms of smooth four-manifolds diagonalize over integers, suggesting fundamental constraints on four-dimensional topology.

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Simon Donaldson (1983) studied this question.

synapsesocial.com/papers/6a110b6ccd70b138bf1a14b9 https://doi.org/10.4310/jdg/1214437665

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An application of gauge theory to four-dimensional topology

Key Points

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Implication

Abstract

Discussion

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An application of gauge theory to four-dimensional topology

Key Points

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Implication

Abstract

Discussion

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