Given a smooth simply connected 4-manifold M, we prove that if there is a smoothly embedded 2-torus T inside M, then the SU(2)-Donaldson invariants of M vanish on collections of 2-homology classes, ah of which are orthogonal to [T] and at least two of which are multiples of [T]. From this we deduce obstructions to the representability of 2-homology classes of some algebraic surfaces by smoothly embedded tori, and we compute the group of self-diffeomorphisms of certain 4-manifolds with boundary.

A vanishing theorem for Donaldson invariants

LISCA, PAOLO
1995

Abstract

Given a smooth simply connected 4-manifold M, we prove that if there is a smoothly embedded 2-torus T inside M, then the SU(2)-Donaldson invariants of M vanish on collections of 2-homology classes, ah of which are orthogonal to [T] and at least two of which are multiples of [T]. From this we deduce obstructions to the representability of 2-homology classes of some algebraic surfaces by smoothly embedded tori, and we compute the group of self-diffeomorphisms of certain 4-manifolds with boundary.
Lisca, Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/24807
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