Related papers: Metric groups attached to biextensions

Given a smooth free action of a compact connected Lie group $G$ on a smooth compact manifold $M$, we show that the space of $G$-invariant Riemannian metrics on $M$ whose automorphism group is precisely $G$ is open dense in the space of all…

We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with…

We generalize two of our previous results on abelian definable groups in $p$-adically closed fields to the non-abelian case. First, we show that if $G$ is a definable group that is not definably compact, then $G$ has a one-dimensional…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

The weights for a finite group G with respect to a prime number p where introduced by Jon Alperin, in order to formulate his celebrated conjecture affirming that that the number of G-conjugacy classes of weights of G coincides with the…

Given any quasi-countable, in particular any countable inverse semigroup $S$, we introduce a way to equip $S$ with a proper and right subinvariant extended metric. This generalizes the notion of proper, right invariant metrics for discrete…

We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double of the group ring kG, we show that the self-extension…

We study quadratic form parameters $Q$ over the integers and extended quadratic forms with values in $Q$, which we call $Q$-forms. Certain form parameters $Q$ appeared in Wall's work on the classification of almost closed $(n-1)$-connected…

We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot group. We also prove a Rademacher-type theorem for such limits.

To a special type of grope embedded in 4-space, that we call an admissible grope, we associate a length function for each real number q at least 1. This gives rise to a family of pseudo-metrics d^q, refining the slice genus metric, on the…

We complement the characterization of the graph products of cyclic groups $G(\Gamma, \mathfrak{p})$ admitting a Polish group topology of [9] with the following result. Let $G = G(\Gamma, \mathfrak{p})$, then the following are equivalent:…

We classify equivalence classes of Hopf algebra quotient pairs $(D,\theta)$ of the Drinfeld double $D(G)$ of a finite group scheme $G$ over an algebraically closed field $\mathbf{k}$ of characteristic $p\ge 0$, in terms of group…

Riera proved at arXiv:1412.6964 that the diffeomorphism group of particular compact manifolds are not Jordan by exhibiting subgroups isomorphic to extra-special $p$-groups of exponent $p$ for primes $p$ satisfying some conditions.…

Let g be a complex, simple Lie algebra and t a Cartan subalgebra of g. A new unitary, flat connection on t with values in any finite-dimensional g-module V and simple poles along the root hyperplanes was recently introduced by J. Millson…

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…

For a Poisson manifold $M$ we develop systematic methods to compute its Picard group $Pic(M)$, i.e., its group of self Morita equivalences. We establish a precise relationship between $Pic(M)$ and the group of gauge transformations up to…

We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension $\leq6$, every nice nilpotent Lie group of dimension $\leq7$ and every…

For a profinite group $G$ we describe an abelian group $W_G(R; M)$ of $G$-typical Witt vectors with coefficients in an $R$-module $M$ (where $R$ is a commutative ring). This simultaneously generalises the ring $W_G(R)$ of Dress and…

Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…