Blowups, Slicings and Permutation Groups in Combinatorial Topology (Paperback) (ISBN-13: 9783832529833)

Combinatorial topology is a field of research that lies in the intersection of geometric topology, combinatorics, algebraic topology and polytope theory. The main objects of interest are piecewise linear topological manifolds where the manifold is given as a simplicial complex with some additional combinatorial structure. These objects are called combinatorial manifolds. In this work, elements and concepts of algebraic geometry, such as blowups, Morse theory as well as group theory are translated into the field of combinatorial topology in order to establish new tools to study combinatorial manifolds. These tools are applied to triangulated surfaces, 3- and 4-manifolds with and without the help of a computer. Among other things, a new combinatorial triangulation of the K3 surface, combinatorial properties of normal surfaces, and new combinatorial triangulations of pseudomanifolds with multiply transitive automorphism group are presented.

Author: Jonathan Spreer
ISBN-10: 3832529837
ISBN-13: 9783832529833
Publisher: Logos Verlag Berlin
Language: English
Published: 10/30/2011
Pages: 251
Format: Paperback