On realizing homology classes by maps of restricted complexity
Algebraic Topology
2014-02-26 v2
Abstract
We show that in every codimension greater than one there exists a mod 2 homology class in some closed manifold (of sufficiently high dimension) which cannot be realized by an immersion of closed manifolds. The proof gives explicit obstructions (in terms of cohomology operations) for realizability of mod 2 homology classes by immersions. We also prove the corresponding result in which the word `immersion' is replaced by `map with some restricted set of multi-singularities'.
Cite
@article{arxiv.1111.0249,
title = {On realizing homology classes by maps of restricted complexity},
author = {Mark Grant and Andras Szucs},
journal= {arXiv preprint arXiv:1111.0249},
year = {2014}
}
Comments
13 pages; Final version, to appear in Bull. Lond. Math. Soc