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
1995-01-01
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.File in questo prodotto:
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