English

Rigidity of the $K(1)$-local stable homotopy category

Algebraic Topology 2018-10-11 v2

Abstract

We investigate a new case of rigidity in stable homotopy theory which is the rigidity of the K(1)K(1)-local stable homotopy category Ho(LK(1)Sp)\mathrm{Ho}(L_{K(1)}\mathrm{Sp}) at p=2p=2. In other words, we show that recovering higher homotopy information by just looking at the triangulated structure of Ho(LK(1)Sp)\mathrm{Ho}(L_{K(1)}\mathrm{Sp}) is possible, which is a property that only few interesting stable model categories are known to possess.

Keywords

Cite

@article{arxiv.1807.03175,
  title  = {Rigidity of the $K(1)$-local stable homotopy category},
  author = {Jocelyne Ishak},
  journal= {arXiv preprint arXiv:1807.03175},
  year   = {2018}
}

Comments

16 pages, minor corrections and many small improvements