The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.

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Bibliographic Information

Book Title: Grassmannians and Gauss Maps in Piecewise-Linear Topology
Authors: Norman Levitt
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0084994
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1989
Softcover ISBN: 978-3-540-50756-7Published: 22 February 1989
eBook ISBN: 978-3-540-46078-7Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: V, 203
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Differential Geometry

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Table of contents (11 chapters)

Front Matter

Back Matter

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