Embeddings of -connected -manifolds into

Author:
A. Skopenkov

Journal:
Proc. Amer. Math. Soc. **138** (2010), 3377-3389

MSC (2010):
Primary 57R40, 57Q37; Secondary 57R52

Published electronically:
May 4, 2010

MathSciNet review:
2653966

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Abstract | References | Similar Articles | 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 1-1 correspondence with for .*

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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:
https://doi.org/10.1090/S0002-9939-10-10425-0

Keywords:
Embedding,
self-intersection,
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.