Related papers: Analytic Topology of Groups, Actions, Strings and …

Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$, assign a number $p(A)\in [0,1]$ for any subset $A$ of $X$. We can interpret $p(A)$ as the probability of openness of…

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…

In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…

We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.

The abstract will be added in due course.

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

Topological characterization of torus groups is given.

This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

The note complements topological aspects of the theory of chiral algebras.

This is a survey recent works on topological extensions of the Tutte polynomial.

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

My work with Anatoly Vershik concerned automorphism groups of the Rado graph and homeomorphism groups of the Urysohn space. This paper contains some further thoughts on these issues, together with connections to topologies and filters on…

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…

This is a survey article devoted to the study of real structures on complex algebraic varieties endowed with a reductive group action.

In this paper, we construct a comparison map from the topological fundamental group to the pro-\'etale fundamental group for a complex variety.

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups.…