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Displaying 1821 –
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Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on with possible fixed points. This restricts the topology of . In all cases, a harmonic morphism from a closed...
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of...
By means of branched coverings techniques, we prove that the Heegaard genus and the regular genus of an orientable 3-manifold with boundary coincide.
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