5 search hits
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Euclidean decompositions of hyperbolic manifolds and their duals
(1998)
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Sascha Georg Lukac
- Epstein and Penner constructed in [EP88] the Euclidean decomposition of a non-compact hyperbolic n-manifold of finite volume for a choice of cusps, n >= 2. The manifold is cut along geodesic hyperplanes into hyperbolic ideal convex polyhedra. The intersection of the cusps with the Euclidean decomposition determined by them turns out to be rather simple as stated in Theorem 2.2. A dual decomposition resulting from the expansion of the cusps was already mentioned in [EP88]. These two dual hyperbolic decompositions of the manifold induce two dual decompositions in the Euclidean structure of the cusp sections. This observation leads in Theorems 5.1 and 5.2 to easily computable, necessary conditions for an arbitrary ideal polyhedral decomposition of the manifold to be a Euclidean decomposition.
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Homfly skeins and the Hopf link
(2001)
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Sascha Georg Lukac
- This thesis exhibits skeins based on the Homfly polynomial and their relations to Schur functions. The closures of skein-theoretic idempotents of the Hecke algebra are shown to be specializations of Schur functions. This result is applied to the calculation of the Homfly polynomial of the decorated Hopf link. A closed formula for these Homfly polynomials is given. Furthermore, the specialization of the variables to roots of unity is considered. The techniques are skein theory on the one side, and the theory of symmetric functions in the formulation of Schur functions on the other side. Many previously known results have been proved here by only using skein theory and without using knowledge about quantum groups.
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Über allgemeine Gesetzmäßigkeiten des Geschehens
(1920)
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Arthur Schoenflies
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Bachelor und Master in Mathematik
(2011)
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Über die geistige Eigenart des Mathematikers : Rede anläßlich der Gründungsfeier des Deutschen Reiches am 18. Januar 1928
(1928)
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Max Dehn
- Enthält auch: Drevermann, Fritz : Bericht über die Preisarbeiten des Jahres 1927 und Bekanntgabe der Preisaufgaben für 1928 durch den Rektor Prof. Dr. Drevermann
