Algebra/Topology Seminar

Speaker: Sam Nariman

Title: On the finiteness of the classifying space of diffeomorphisms of reducible three manifolds

Abstract: It is known that the classifying space BDiff(S, rel boundary) for a surface S with a nontrivial boundary is homotopy equivalent to a finite CW complex e.g. the corresponding moduli space of Riemann surfaces. Similarly, in dimension 3, there is a conjecture that on Kirby's list is attributed to Kontsevich which says that the classifying space BDiff(M, rel boundary) for any 3-manifold with a non-empty boundary has a finite dimensional model. When M is irreducible, this conjecture was solved by Hatcher-McCullough. In this talk we discuss the case where M is reducible with distinct irreducible factors.

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