Reeb spaces of piecewise linear mappings

Generalizing the concept of a Reeb graph, the Reeb space of a multivariate continuous mapping identifies points of the domain that belong to a common component of the preimage of a point in the range. We study the local and global structure of this space for generic, piecewise linear mappings on a combinatorial manifold. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Computations on discrete structures, Geometrical problems and computations General Terms Algorithms, Theory Keywords Smooth and PL topology, combinatorial manifolds, Reeb spaces, cone neighborhoods, triangulations, stratifications, algorithms.

• Type: Conference
• Year: 2008
• Where: COMPGEOM
• Authors: Herbert Edelsbrunner, John Harer, Amit K. Patel
• Keywords: Combinatorial Manifolds, COMPGEOM 2008, Discrete Geometry, Reeb Graph, Reeb Spaces