Reeb spaces of piecewise linear mappings

Authors:
Herbert Edelsbrunner;John Harer;Amit K. Patel
Affiliations:
Duke University, Durham, NC, USA;Duke University, Durham, NC, USA;Duke University, Durham, NC, USA
Venue:
Proceedings of the twenty-fourth annual symposium on Computational geometry
Year:
2008

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Abstract

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.