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Algebraic and Geometric Surgery$
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Algebraic and Geometric Surgery

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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COBORDISM THEORY

COBORDISM THEORY

Chapter:
(p.124) 6 COBORDISM THEORY
Source:
Algebraic and Geometric Surgery
Author(s):

Andrew Ranicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509240.003.0006

Two manifolds are cobordant if, and only if, one can be transformed to the other by a sequence of surgeries. This chapter discusses the Pontrjagin-Thom transversality isomorphism between the cobordism groups and homotopy groups. Computations of framed, unoriented, and oriented cobordism are also mentioned. The signature is the basic cobordism invariant.

Keywords:   transversality, framed cobordism, unoriented cobordism, oriented cobordism, signature

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