Hamiltonian Submanifolds of Regular Polytopes

Released on by Felix Effenberger
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  • Hamiltonian Submanifolds of Regular Polytopes Book Detail

  • Author : Felix Effenberger
  • Release Date : 2011
  • Publisher : Logos Verlag Berlin GmbH
  • Genre : Mathematics
  • Pages : 224
  • ISBN 13 : 3832527583
  • File Size : 39,39 MB
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Hamiltonian Submanifolds of Regular Polytopes by Felix Effenberger PDF Summary

Book Description: This work is set in the field of combinatorial topology, sometimes also referred to as discrete geometric topology, a field of research in the intersection of topology, geometry, polytope theory and combinatorics. The main objects of interest in the field are simplicial complexes that carry some additional structure, forming combinatorial triangulations of the underlying PL manifolds. In particular, polyhedral manifolds as subcomplexes of the boundary complex of a convex regular polytope are investigated. Such a subcomplex is called k-Hamiltonian if it contains the full k-skeleton of the polytope. The notion of tightness of a PL-embedding of a triangulated manifold is closely related to its property of being a Hamiltonian subcomplex of some convex polytope. Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is ``as convex as possible''. It can thus be understood as a generalization of the concept of convexity. In even dimensions, there exist purely combinatorial conditions which imply the tightness of a triangulation. In this work, other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well are presented.

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Polytopes

Polytopes

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The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The arti