What question did this study set out to answer?

Determine the algebraic structure of the intersection form on compact, simply connected, oriented smooth 4-manifolds with positive-definite intersection forms.

January 1, 1983Journal of Differential GeometryOpen Access

An application of gauge theory to four-dimensional topology

View Full Paper

Ask AI

Bookmark

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.

Implication

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

Abstract

Soit X une u-variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee Q est definie positive. Alors cette forme est equivalente, sur les entiers, a la forme diagonale standard, soit dans une base: Q(u 1 ,u 2 ,...u 2 )=u 2 1 +u 2 2 +...+u 2 2

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Simon Donaldson (1983) studied this question.

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

View Full Paper

Ask AI

Bookmark

Implication

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

An application of gauge theory to four-dimensional topology

Key Points

Implication

Abstract

Discussion

Cite This Study

An application of gauge theory to four-dimensional topology

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading