Lattices, embeddings and Seifert fibered spaces.

Lattices, embeddings and Seifert fibered spaces.

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Duncan McCoy
Taplin Auditorium

Every Seifert fibered homology sphere bounds a definite star-shaped plumbing. In 1985 Neumann and Zagier used the R-invariant of Fintushel and Stern to show that a Seifert fibered homology sphere can smoothly bound a homology ball only when the central vertex of this definite plumbing has weight \pm 1. They then asked whether Donaldson's theorem can be used to obtain the same result. I will discuss joint work with Ahmad Issa showing how Neumann and Zagier's question can be answered in the affirmative and how, in fact, Donaldson's theorem yields stronger conclusions than the R-invariant. I will also explain applications of our techniques to the question of which Seifered fibered spaces embed in S^4.