Related papers: Lifting $N_\infty$ operads from conjugacy data

Let G be a connected reductive group. We define a map from the set of unipotent classes in G to the set of conjugacy classes in the Weyl group (assuming that the characteristic is not bad). This map is a one sided inverse of a map in the…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…

Let G be a connected reductive group over an algebraically closed field. We define a decomposition of G into finitely many strata such that each stratum is a union of conjugacy classes of fixed dimension; the strata are indexed by a set…

To every homotopy n-nilpotent group, defined in earlier work by Dwyer and the author, we associate an endofunctor of pointed spaces and prove that it is looped and n-excisive. As a tool we prove that $\Omega P_n({\rm id})$ commutes with…

We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…

In this paper we study conjugacy and subgroup separability properties in the class of nilpotent $\mathbb{Q}[x]$-powered groups. Many of the techniques used to study these properties in the context of ordinary nilpotent groups carry over…

This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.

Many results have been established that show how arithmetic conditions on conjugacy class sizes affect group structure. A conjugacy class in $G$ is called vanishing if there exists some irreducible character of $G$ which evaluates to zero…

Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self-maps of spaces related to the given objects. Here we address a question posed by Gon\c{c}alves and…

The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divides the other. We determine the connected components of the…

Let G' be a connected reductive group over the complex numbers. We show that the set of conjugacy classes of G' is in natural bijection with the set of two-sided cells associated to a certain algebra.

Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes of G.

Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…

Let $G$ be a finite group. This expository article explores the subject of commuting probability in the group $G$ and its relation with simultaneous conjugacy classes of commuting tuples in $G$. We also point out the relevance of this topic…

In the paper we study twisted conjugacy classes and isogredience classes for automorphisms of reductive linear algebraic groups. We show that reductive linear algebraic groups over some fields of zero characteristic possess the $R_\infty$…

We discuss the existence of Gribov ambiguities in $SU(m)\times U(1)$ gauge theories over the $n-$spheres. We achieve our goal by showing that there is exactly one conjugacy class of groups of gauge transformations for the theories given…

We classify the conjugacy classes of minimally ramified nonabelian subgroups of order 8 in the Nottingham group $N(F_4)$. We then use finite automata to give explicit descriptions of representatives for each of these conjugacy classes.

We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a…

In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.