Embeddings of connected manifolds into
Author:
A. Skopenkov
Journal:
Proc. Amer. Math. Soc. 138 (2010), 33773389
MSC (2010):
Primary 57R40, 57Q37; Secondary 57R52
Published electronically:
May 4, 2010
MathSciNet review:
2653966
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Additional Information
Abstract: We obtain estimations for isotopy classes of embeddings of closed connected manifolds into for and . This is done in terms of an exact sequence involving the Whitney invariants and an explicitly constructed action of on the set of embeddings. The proof involves a reduction to the classification of embeddings of a punctured manifold and uses the parametric connected sum of embeddings. Corollary. Suppose that is a closed almost parallelizable connected manifold and . Then the set of isotopy classes of embeddings is in 11 correspondence with for .
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 D. Crowley and A. Skopenkov, A classification of smooth embeddings of manifolds in space, II, submitted, arXiv:math/0808.1795.
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Additional Information
A. Skopenkov
Affiliation:
Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119992 – and – Independent University of Moscow, B. Vlasyevskiy, 11, 119002, Moscow, Russia
Email:
skopenko@mccme.ru
DOI:
http://dx.doi.org/10.1090/S0002993910104250
PII:
S 00029939(10)104250
Keywords:
Embedding,
selfintersection,
isotopy,
parametric connected sum
Received by editor(s):
December 16, 2008
Received by editor(s) in revised form:
December 31, 2009
Published electronically:
May 4, 2010
Communicated by:
Alexander N. Dranishnikov
Article copyright:
© Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
