Some Problems on Knots, Braids, and Automorphism Groups

TL;DR

This paper discusses open problems in the mathematical study of knots, braids, and automorphism groups, highlighting challenges and questions in group properties, braid structures, hyperbolic 3-orbifold groups, and symmetric cohomology.

Contribution

It compiles and explores several open problems in knot theory, braid groups, and automorphism groups, providing a foundation for future research in these areas.

Findings

Identification of open problems in palindromic and commutator widths

Analysis of properties of Brunnian and two-colored braids

Discussion of hyperbolic 3-orbifold groups and automorphisms

Abstract

We present and discuss some open problems formulated by participants of the International Workshop "Knots, Braids, and Auto\-mor\-phism Groups" held in Novosibirsk, 2014. Problems are related to palindromic and commutator widths of groups; properties of Brunnian braids and two-colored braids, corresponding to an amalgamation of groups; extreme properties of hyperbolic 3-orbifold groups, relations between inner and quasi-inner automorphisms of groups; and Staic's construction of symmetric cohomology of groups.