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Heegaard splittings, the curve complex, and hyperbolic geometry
Defined by Poul Heegaard in his thesis in 1898, Heegaard splittings of three-manifolds are still not completely understood. There are deep connections between these decompositions of three-manifolds and the algebraic, combinatorial, and geometric structure of the ambient space. I will discuss just a few of these connections while outlining the "modern" theory of Heegaard splittings. This dates from Casson and Gordon's introduction of "strong irreducibility" in their 1987 paper.
Thursday, February 19, 2004, 445 Altgeld Hall, 2:00 p.m.
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