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# ðŸ“™ Grassmannians and Gauss Maps in Piecewise-Linear and Piecewise-Differential Topology by Norman Levitt â€” pdf free

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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.

## About book:

## About file:

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- Series:
**Lecture Notes in Mathematics** - Author:
**Norman Levitt** - Year:
**1989** - Publisher:
**Springer** - Language:
**English** - ISBN:
**3540507566,9783540507567**

- File size:
**6 399 617** - Format:
**pdf**

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The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of...

2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . ....

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 Grassma...

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By mean...

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of its own and as an approach to control theory. The book deals with the theory of semi-linear differential inclusions in infinite dimensional spaces....

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of its own and as an approach to control theory. The book deals with the theory of semi-linear differential inclusions in infinite dimensional spaces....

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the...

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the...

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means...