Embeddings in the 3/4 range

Details Embeddings in the 3/4 range Embeddings in the 3/4 range

2003-11-24

arxiv.org/abs/math/0311423v2

Mathematics

Algebraic Topology

33 pages, extensively rewritten due to incorporation of comments by the referee

Scientific paper

We give a complete obstruction to turning an immersion of an m-dimensional manifold M in Euclidean n-space into an embedding when 3n>4m+4. It is a secondary obstruction, and exists only when the primary obstruction, due to Haefliger, vanishes. The obstruction lives in a twisted cobordism group, and its vanishing implies the existence of an embedding in the regular homotopy class of the given immersion in the range indicated. We use Goodwillie's calculus of functors, following Weiss, to help organize and prove the result.

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