The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations

Piotr Beben; Stephen Theriault

The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations

Algebraic Topology 2014-06-04 v1 Geometric Topology

Authors: Piotr Beben , Stephen Theriault

Abstract

We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$ -connected $2n$ -dimensional manifolds provided $n\notin\{4,8\}$ , and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free $CW$ -complexes with well-behaved skeleta and some Poincar\'{e} duality features.

Keywords

loop space homotopy type four-manifolds simply-connected CW-complexes Poincaré duality connected sum

Cite

@article{arxiv.1406.0651,
  title  = {The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations},
  author = {Piotr Beben and Stephen Theriault},
  journal= {arXiv preprint arXiv:1406.0651},
  year   = {2014}
}

Comments

Adv. Math., to be published

The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations

Abstract

Keywords

Cite

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