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Modeling Stable One-Types.

Mon, 01/16/2012 - 15:01 — SomNambul
Authors: Niles Johnson, Angélica M. Osorno
Subjects: Algebraic Topology
link: http://arxiv.org/abs/1201.2686
Abstract

It is a classical result that groupoids model homotopy 1-types, in the sense
that there is an equivalence between the homotopy categories, via the
classifying space and fundamental groupoid functors. We extend this to stable
homotopy 1-types and Picard groupoids.

Using an algebraic description of Picard groupoids, we give a model for the
Postnikov invariant of a stable 1-type and describe the action of the truncated
sphere spectrum in these terms. We relate this data to exact sequences of
Picard groupoids developed by Vitale, constructing a model for the homotopy
cofiber of a map of stable 1-types.

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Wed, 01/18/2012 - 05:21 — chendan

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