On the homotopy classification of spaces by the fixed loop space homology

Samson Saneblidze

On the homotopy classification of spaces by the fixed loop space homology

Algebraic Topology 2010-03-16 v1

Authors: Samson Saneblidze

Abstract

Let $R\subseteq \Bbb Q$ be a subring of the rationals and let $p$ be the least prime (if none, $p=\infty$ ) which is not invertible in $R.$ For an $R$ -local $r$ -connected $CW$ -complex $X$ of dimension $\leq \min(r+2p-3,rp-1), r\geq 1,$ a complete homotopy invariant is constructed in terms of the loop space homology $H_*(\Omega X).$ This allows us to classify all such $R$ -local spaces up to homotopy with a fixed loop space homology.

Keywords

homotopy classification loop space homology R-local spaces CW-complex homotopy invariant

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@article{arxiv.1003.2897,
  title  = {On the homotopy classification of spaces by the fixed loop space homology},
  author = {Samson Saneblidze},
  journal= {arXiv preprint arXiv:1003.2897},
  year   = {2010}
}

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8 pages

On the homotopy classification of spaces by the fixed loop space homology

Abstract

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