Unstable Adams operations on p-local compact groups

Fabien Junod, Ran Levi, Assaf Libman

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A $p$-local compact group is an algebraic object modeled on the $p$-local homotopy theory of classifying spaces of compact Lie groups and $p$-compact groups. In the study of these objects unstable Adams operations, are of fundamental importance. In this paper we define unstable Adams operations within the theory of $p$-local compact groups, and show that such operations exist under rather mild conditions. More precisely, we prove that for a given $p$-local compact group $\mathcal{G}$ and a sufficiently large positive integer $m$, there exists an injective group homomorphism from the group of $p$-adic units which are congruent to 1 modulo $p^m$ to the group of unstable Adams operations on $\mathcal{G}$.
Original languageEnglish
Pages (from-to)49-74
Number of pages26
JournalAlgebraic & Geometric Topology
Volume12
Issue number1
Early online date31 Mar 2011
DOIs
Publication statusPublished - 24 Jan 2012

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Adams Operations
Compact Group
Unstable
P-compact Group
Algebraic object
Classifying Space
Homotopy Theory
Compact Lie Group
Congruent
P-adic
Injective
Homomorphism
Modulo
Unit
Integer

Keywords

  • classifying space
  • p-local compact groups
  • unstable Adams operation

Cite this

Unstable Adams operations on p-local compact groups. / Junod, Fabien; Levi, Ran; Libman, Assaf.

In: Algebraic & Geometric Topology, Vol. 12, No. 1, 24.01.2012, p. 49-74.

Research output: Contribution to journalArticle

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