English

Umkehr Maps Patched via the Compactified Cleavage Operad

Algebraic Topology 2014-12-10 v3

Abstract

Via a compactification of the cleavage operad, we describe two actions on the mapping spaces from spheres into compact, oriented manifolds. The map from the compactified version of the cleavage operad provides a version of intersection theory along the underlying base manifold lifted to the mapping space. The other action map only works for the uncompactified cleavage operad, and gives a homotopy theoretic version of higher dimensional string topology.

Keywords

Cite

@article{arxiv.1206.5842,
  title  = {Umkehr Maps Patched via the Compactified Cleavage Operad},
  author = {Tarje Bargheer},
  journal= {arXiv preprint arXiv:1206.5842},
  year   = {2014}
}

Comments

This paper is under revision since there is a mistake not taking twistings into account. An upcoming paper with a different scope solves this problem in a geometric fashion. The statements on the compactifications in this paper will be reformulated accordingly