Talk page
Title:
Intersection forms of smooth 4-manifolds with boundary
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Abstract:
In a smooth compact 4-manifold, the intersection of 2-dimensional cycles defines the structure of an integral lattice on its second homology. In the early 1980's, Donaldson showed that if the 4-manifold has no boundary and its lattice is definite, then it must be diagonalizable over the integers. However, this is not the case if the 4-manifold has boundary. Yang-Mills instanton and Seiberg-Witten gauge theory give constraints on the possibilities, and sometimes a classification of lattices bounded by a fixed 3-manifold is achieved. In this talk, we will focus on the case in which the boundary has the same homology as the 3-sphere, and give a survey to previous work on this problem, as well as present some new results.
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