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On the Classification of Manifolds Up to Finite Ambiguity

Published online by Cambridge University Press:  20 November 2018

Matthias Kreck  and
Georgia Triantafillou
Matthias Kreck
Affiliation:
Fachbereich Mathematik University Mainz Mainz, West Germany
Georgia Triantafillou
Affiliation:
Department of Mathematics University of Crete Crete, Greece
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In the early 70's Dennis Sullivan applied his theory of minimal models and surgery to the classification of 1-connected closed smooth manifolds of dimension ≥ 5 up to finite ambiguity [Su]. To a diffeomorphism class of such a manifold M he assigns the isomorphism class given by the real minimal model ℳ (M), the integral structure in form of various lattices and the real Pontryagin classes. If one controls the torsion of the manifolds by some bound, his result is that the map given by the triple above is finite-to-one ([Su], Theorem 13.1). He also proves a realization result for the rational minimal model and the Pontryagin classes but not for the lattices ([Su], Theorem 13.2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 356 - 370
Copyright
Copyright © Canadian Mathematical Society 1991

References

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