Homotopy type of the complement of an immersion and classification of embeddings of tori

Details Homotopy type of the complement of an immersion and classification of embeddings of tori Homotopy type of the complement of an immersion and classification of embeddings of tori

2008-03-29

arxiv.org/abs/0803.4285v1

Russian Math. Surv. 62:5 (2007), 985-987

Mathematics

Geometric Topology

Scientific paper

10.1070/RM2007v062n05ABEH004468

This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings $S^p\times S^q\to S^m$, which we call knotted tori. The set of knotted tori in the the space of sufficiently high dimension, namely in the metastable range $m\ge p+3q/2+2$, $p\le q$, which is a natural limit for the classical methods of embedding theory, has been explicitely described earlier. The aim of this note is to present an approach which allows for results in lower dimension.

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