Handlebody splittings of compact 3-manifolds with boundary.

Shin'ichi Suzuki

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Displaying similar documents to “Handlebody splittings of compact 3-manifolds with boundary.”

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In this paper we construct, for each aspherical oriented $3$ -manifold $M$ , a $2$ -dimensional class in the $l_{1}$ -homology of $M$ whose norm combined with the Gromov simplicial volume of $M$ gives a characterization of those nonzero degree maps from $M$ to $N$ which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of $M$ and $N$ .

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These notes accompany some lectures given at the autumn school “” in October 2009. The abelian Reidemeister torsion for $3$ -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.

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Multiple prime covers of the riemann sphere

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A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.