On the Generating Hypothesis in Noncommutative Stable Homotopy
arXiv:1302.2051 · doi:10.7146/math.scand.a-21164
Abstract
Freyd's Generating Hypothesis is an important problem in topology with deep structural consequences for finite stable homotopy. Due to its complexity some recent work has examined analogous questions in various other triangulated categories. In this short note we analyze the question in noncommutative stable homotopy, which is a canonical generalization of finite stable homotopy. Along the way we also discuss Spanier--Whitehead duality in this extended setup.
6 pages; v2 added a Section on Matrix Generating Hypothesis; v3 included Spanier--Whitehead duality discussion and removed some unnecessary material, to appear in Math. Scand; v4 updated references and metadata