Abstract
During the 1980’s, Simon Donaldson utilized the Yang-Mills equations, which had originated in mathematical physics, to study the differential topology of four-manifolds. Using work of Michael Freedman, he was able to prove theorems of the following type:
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Theorem A.
There exist many compact topological four-manifolds which have no smooth structure.
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Theorem B.
There exist many pairs of compact simply connected smooth four-manifolds which are homeomorphic but not diffeomorphic.
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Preliminaries. In: Lectures on Seiberg-Witten Invariants. Lecture Notes in Mathematics, vol 1629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40952-6_1
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DOI: https://doi.org/10.1007/978-3-540-40952-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41221-2
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