Finite approximations of $p$-local compact groups
Alex Gonzalez

TL;DR
This paper demonstrates that the classifying space of a $p$-local compact group can be approximated by a sequence of classifying spaces of $p$-local finite groups, leading to new insights in homotopy theory.
Contribution
It introduces a method to approximate $p$-local compact groups using telescopes of $p$-local finite groups, with implications for stable elements and mapping spaces.
Findings
Classifying space of $p$-local compact group approximated by telescope of finite groups
Stable Elements Theorem extended to $p$-local compact groups
Homotopy types of certain mapping spaces characterized
Abstract
We show that the classifying space of a -local compact group is approximated by a telescope of classifying spaces of -local finite groups. This result has numerous implications, like a Stable Elements Theorem for -local compact groups, or the description of the homotopy type of certain mapping spaces.
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