Embeddings in the 3/4 range
Algebraic Topology
2007-05-23 v2 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0311423,
title = {Embeddings in the 3/4 range},
author = {Brian A. Munson},
journal= {arXiv preprint arXiv:math/0311423},
year = {2007}
}
Comments
33 pages, extensively rewritten due to incorporation of comments by the referee