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Algebraic and Geometric Surgery$
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Andrew Ranicki

Print publication date: 2002

Print ISBN-13: 9780198509240

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198509240.001.0001

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EMBEDDINGS, IMMERSIONS, AND SINGULARITIES

EMBEDDINGS, IMMERSIONS, AND SINGULARITIES

Chapter:
(p.142) 7 EMBEDDINGS, IMMERSIONS, AND SINGULARITIES
Source:
Algebraic and Geometric Surgery
Author(s):

Andrew Ranicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509240.003.0007

This chapter describes the algebraic and geometric intersection properties of submanifolds used to establish the one-one correspondence between algebraic and geometric surgeries below the middle dimension. The Whitney immersion and embedding theorems are required for this purpose, and for analysing the obstructions in the middle dimension.

Keywords:   Whitney immersion theorem, Whitney embedding theorem, algebraic intersection, geometric intersection, Whitney trick, Smale-Hirsch classification of immersions, singularities

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