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Alex Gonzalez

Publications and source records attributed to Alex Gonzalez.

11 recordsLinked to original sources
arXiv2021

An extension theory for partial groups

Partial groups are a natural generalization of discrete groups recently introduced by Chermak in connection with the theory of fusion systems. In this paper we develop an extension theory for partial groups based in the classical theory of fibre bundles of simplicial sets.

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arXiv2017

Discrete Localities I

This is part I of a three-part series of papers, whose aim is to develop a theory of discrete localities. These generalize the p-local compact groups of Broto, Levi, and Oliver.

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arXiv2015

Some new examples of simple $p$-local compact groups

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can be applied in a more general framework.

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arXiv2015

Euler characteristic for weak n-categories and $\left(\infty,1\right)$-categories

The Euler characteristic was defined for finite strict n-categories by Leinster using the theory of enriched categories. This was an extension of some of his earlier work, which defined Euler characteristic for finite categories. Building on Leinster's work, we extend the notion of Euler characteristic to certain finite weak 2-categories and present a sketch of a similar extension to weak n-categories. We also discuss the extension of the Euler characteristic to certain finite $\left(\infty,1\right)$-categories.

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arXiv2015

Automorphisms of $p$-local compact groups

Self equivalences of classifying spaces of $p$-local compact groups are well understood by means of the algebraic structure that gives rise to them, but explicit descriptions are lacking. In this paper we use a construction of Robinson of an amalgam $G$, realizing a given fusion system, to produce a split epimorphism from the outer automorphism group of $G$ to the group of homotopy classes of self homotopy equivalences of the classifying space of the corresponding $p$-local compact group.

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arXiv2015

An extension theory for partial groups and localities

A partial group is a generalization of the concept of group recently introduced by A. Chermak. By considering partial groups as simplicial sets, we propose an extension theory for partial groups using the concept of (simplicial) fibre bundle. This way, the classical extension theory for groups naturally extends to an extension theory of partial groups. In particular, we show that the category of partial groups is closed by extensions. We also describe the cohomological obstructions for existence and uniqueness of extensions, generalizing the usual obstructions for group extensions. The second part of the paper considers extensions of (finite) localities, which are a particular type of partial group, mimicking the p-local structure of finite groups. The goal here is to give sufficient conditions for an extension of localities to produce a new locality.

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arXiv2015

Finite approximations of $p$-local compact groups

We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact groups, or the description of the homotopy type of certain mapping spaces.

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