Related papers: Equivariant homotopy commutativity for $G=C_{pqr}$

The article deals with finite groups in which commutators have prime power order (CPPO-groups). We show that if G is a soluble CPPO-group, then the order of the commutator subgroup G' is divisible by at most two primes.

We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori.…

In this paper, first we obtain an explicit formula for an outer commutator multiplier of nilpotent products of cyclic groups with respect to the variety $[\mathfrak{N}_{c_1},\mathfrak{N}_{c_2}]$, $\mathfrak{N}_{c}M(\mathbb{Z}\st{n}*…

Clifford quantum circuits are elementary invertible transformations of quantum systems that map Pauli operators to Pauli operators. We study periodic one-parameter families of Clifford circuits, called loops of Clifford circuits, acting on…

Let $g$ be an even positive integer, and $p$ be a prime number. We compute the cohomological invariants with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of the stacks of hyperelliptic curves $\mathscr{H}_g$ over an algebraically closed field…

We express the set of representations from a cyclic $p$-group to a connected $p$-compact group in terms of the associated reflection group and compute its cardinality for each exotic $p$-compact group.

We prove that the $v_1$-local $G$-equivariant stable homotopy category for $G$ a finite group has a unique $G$-equivariant model at $p=2$. This means that at the prime $2$ the homotopy theory of $G$-spectra up to fixed point equivalences on…

We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…

Let G,H be closed permutation groups on an infinite set X, with H a subgroup of G. It is shown that if G and H are orbit-equivalent, that is, have the same orbits on the collection of finite subsets of X, and G is primitive but not…

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We…

This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\alpha…

For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…

In this paper we study various simplicial complexes associated to the commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the complex associated to the poset of pairwise non-commuting (resp. commuting) sets in G. We…

We describe the integral cohomology of $X/G$ where $X$ is a compact complex manifold and $G$ a cyclic group of prime order with only isolated fixed points. As a preliminary step, we investigate the integral cohomology of toric blow-ups of…

Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. Associate a graph $\Gamma_G$ (called non-commuting graph of $G$) with $G$ as follows: take $G\setminus Z(G)$ as the vertices of $\Gamma_G$ and join two distinct vertices $x$…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…

Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of…

Let $G$ be a compact, simply connected Lie group. If $\mathcal{C}_1,\mathcal{C}_2$ are two $G$-conjugacy classes, then the set of elements in $G$ that can be written as products $g=g_1g_2$ of elements $g_i\in \mathcal{C}_i$ is invariant…