Related papers: Problems In Groups, Geometry, and Three-Manifolds

This paper poses some basic questions about instances (hard to find) of a special problem in 3-manifold topology. "Important though the general concepts and propositions may be with the modern industrious passion for axiomatizing and…

Adyan and Rabin showed that most properties of groups cannot be algorithmically recognized from a finite presentation alone. We prove that, if one is also given a solution to the word problem, then the class of fundamental groups of closed,…

We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

These notes grew out of a lecture series given at RIMS in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold…

For any given finitely presented group G there exists a closed oriented 4-manifold with fundamental group G. What pairs of integers can occur as the signature and Euler characteristic of such a 4-manifold? The first part of this paper…

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field…

In this survey we discuss how geometric methods can be used to study topological properties of 3-manifolds such as their Heegaard genus or the rank of their fundamental group. On the other hand, we also discuss briefly some results relating…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…

This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learning". The competition asked participants to provide…

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

These are the open problems presented at the 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA13), Gaithersburg, Maryland, on June 4, 2015.

In the present paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups…

Open problems in information geometry are collected and discussed in the conference ``Further Developments of Information Geometry (FDIG) 2025'' held at the University of Tokyo, Japan, from March 18 to 21, 2025.

The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schr\"odinger Institute on July 17-21. These are the problems that were proposed during the Problem Session:…

This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative…

We have proved in [Topology, 45 1 (2006)] that fundamental groups of oriented geometrizable 3-manifolds have a solvable conjugacy problem. We now consider the case of groups of non-oriented geometrizable 3-manifolds in order to conclude…