Publications of the Research Institute for Mathematical Sciences


Full-Text PDF (368 KB) | Metadata | Table of Contents | PRIMS summary
Volume 50, Issue 3, 2014, pp. 497–513
DOI: 10.4171/PRIMS/142

Published online: 2014-09-17

Generalized Bousfield Lattices and a Generalized Retract Conjecture

Ryo Kato[1], Katsumi Shimomura[2] and Yutaro Tatehara[3]

(1) Nagoya University, Japan
(2) Kochi University, Japan
(3) Kochi University, Japan

In [1], Bousfi eld studied a lattice (Bousfi eld lattice) on the stable homotopy category of spectra, and in [5], Hovey and Palmieri made the retract conjecture about that lattice. In this paper we generalize the Bousfi eld lattice and the retract conjecture to ones on a monoid. We also determine the structure of typical examples of generalized Bous field lattices which satisfy the generalized retract conjecture. In particular we give explicitly the structure of the Bousfi eld lattice of the stable homotopy category of harmonic spectra.

Keywords: stable homotopy category, Bousfield lattice, retract conjecture

Kato Ryo, Shimomura Katsumi, Tatehara Yutaro: Generalized Bousfield Lattices and a Generalized Retract Conjecture. Publ. Res. Inst. Math. Sci. 50 (2014), 497-513. doi: 10.4171/PRIMS/142