相关论文: The space of commuting n-tuples in SU(2)

We compute the cohomology of the unordered configuration spaces of the sphere $S^2$ with integral and with $\mathbb{Z}/p \mathbb{Z}$-coefficients using a cell complex by Fuks, Vainshtein and Napolitano.

We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of $S^k \times S^l$, where $3 \le k < l \le 2k - 2$. The result is expressed in terms of Lie graph complex…

In these notes we study left-invariant involutive structures on $\mathrm{SU}(2)$, the most na\"ive non-commutative compact Lie group. We determine closedness of the range (in the smooth topology) of a single complex vector field spanning…

We analyse the homotopy types of gauge groups for principal $U(n)$-bundles over lens spaces.

We investigate the geometry of the space of N-valent SU(2)-intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are…

A result of Jost and Zuo is used to show that for a large class of finite-dimensional hyperk\"ahler quotients, the only L2 harmonic forms lie in the middle dimension, and are of type (k,k) with respect to all complex structures. The…

Let $\mathbf{B}PU_{n}$ be the classifying space of $PU_n$, the projective unitary group of order $n$, for $n>1$. We use the Serre spectral sequence associated to a fiber sequence $\mathbf{B}U_n\rightarrow\mathbf{B}PU_n\rightarrow…

We compute the integral homology of the space of paths in $\mathbb{C}P^n$ with endpoints in $\mathbb{R}P^n$, $n \ge 1$ and its algebra structure with respect to the Pontryagin-Chas-Sullivan product with $\mathbb{Z}/2$-coefficients.

For a fixed $N$, we analyze the space of all sequences $z=(z_1,\dots,z_N)$, approximating a continuous function on the circle, with a given persistence diagram $P$, and show that the typical components of this space are homotopy equivalent…

In this article we determine the stable cohomology groups H^i_s (A_n, Z/p) of the alternating groups A_n for all integers n and i, and all primes p.

Dwyer, Miller and Wilkerson proved that at the prime 2, the classifying spaces of SU(2) and SO(3) can be obtained as a homotopy pushout of the classifying spaces of certain subgroups. In this paper we show explicitly how these…

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…

For $n\in\{2^t-3,2^t-2,2^t-1\}$ ($t\ge3$) we study the cohomology algebra $H^*(\widetilde G_{n,3};\mathbb Z_2)$ of the Grassmann manifold $\widetilde G_{n,3}$ of oriented $3$-dimensional subspaces of $\mathbb R^n$. A complete description of…

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate…

Let $\mathcal{G}_{k,n}$ be the gauge group of the principal $\mathrm{Sp}(n)$-bundle over $S^4$ corresponding to $k\in\mathbb{Z}\cong\pi_3(\mathrm{Sp}(n))$. We refine the result of Sutherland on the homotopy types of $\mathcal{G}_{k,n}$ and…

Let Gamma\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D_0 is a Gamma-equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Gamma. We explicitly construct a…

Z(n) monopoles are important for the understanding of Goddard-Nuyts-Olive duality when the scalar field is not in the adjoint representation. We analyze the Z(2) monopole solutions in a SU(n) Yang-Mills-Higgs theory spontaneously broken to…

The holomorphic homogeneous prepotential encoding the special geometry of the special K\"ahler manifolds ${\textstyle SU(1,n)\over \textstyle U(1)\otimes SU(n)}$ is constructed using the symplectic embedding of the isometry group $SU(1,n)$…

Let $P^{2n+1}$ be a two-cell complex which is formed by attaching a $(2n+1)$--cell to a $2m$--sphere by a suspension map. We construct a universal space $U$ for $P^{2n+1}$ in the category of homotopy associative, homotopy commutative…

In this paper we study homological stability for spaces ${\rm Hom}(\mathbb{Z}^n,G)$ of pairwise commuting $n$-tuples in a Lie group $G$. We prove that for each $n\geqslant 1$, these spaces satisfy rational homological stability as $G$…