Embeddings of k-connected n-manifolds into R^{2n-k-1}

Abstract

We obtain estimations for isotopy classes of embeddings of closed k-connected n-manifolds into R^{2n-k-1} for n>2k+5 and k\ge0. This is done in terms of an exact sequence involving the Whitney invariants and an explicitly constructed action of H_{k+1}(N;Z_2) on the set of embeddings. (For k\ne1 classification results were obtained by algebraic methods without direct construction of embeddings or homology invariants.) The proof involves reduction to classification of embeddings of punctured manifold and uses parametric connected sum of embeddings.

15 pages, no figures, introduction corrected according to recently found reference

References in corpus (3)

• Embedding and knotting of manifolds in Euclidean spaces
• A classification of smooth embeddings of 3-manifolds in 6-space
• Classification of embeddings below the metastable dimension

Cited by in corpus (2)

• Classification of knotted tori
• A description of values of Seifert form for punctured n-manifolds in (2n-1)-space