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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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POINCARÉ DUALITY

POINCARÉ DUALITY

Chapter:
(p.48) 4 POINCARÉ DUALITY
Source:
Algebraic and Geometric Surgery
Author(s):

Andrew Ranicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509240.003.0004

Poincaré duality is an isomorphism between the homology and cohomology of a manifold. The chapter introduces the basic duality and the universal Poincaré duality for non-simply-connected manifolds using the involution on the fundamental group ring. Poincaré duality governs the homological effect of a surgery. The example of surgery on surfaces is given.

Keywords:   effect of surgery, surface, ring with involution, universal Poincaré duality

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