Related papers: Embedding functors and their arithmetic properties

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category. Unitary $R$-matrices, namely unitary solutions to the…

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a…

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere,…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

Suppose that $G$ is the group of $F$-points of a connected reductive group over $F$, where $F/\mathbb{Q}_p$ is a finite extension. We study the (topological) irreducibility of principal series of $G$ on $p$-adic Banach spaces. For unitary…

Given a finitely generated group G, the set Hom(G,SL_2 C) inherits the structure of an algebraic variety R(G)called the "representation variety" of G. This algebraic variety is an invariant of G. Let G_{pt}=< a, b; a^p= b^t>, where p, t are…

It is a classical theorem that the free product of ordered groups is orderable. In this note we show that, using a method of G. Bergman, an ordering of the free product can be constructed in a functorial manner, in the category of ordered…

A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture under the additional assumption that the isometry group has…

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation.…

For a reductive group G defined over an algebraically closed field of positive characteristic, we show that the Frobenius contraction functor of G-modules is right adjoint to the Frobenius twist of the modules tensored with the Steinberg…

We study Goodwillie-Weiss embedding calculus through its relationship with Goodwillie's functor calculus. Specifically, building on a result of Tillmann and Weiss, we construct a functorial complement for \(T_{n}\)-embeddings that takes…

Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric…

We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a…

For a countable group G = <A | R> presented by its generators A and defining relations R we discuss a simple method to embed G into such a 2-generator group T that the images of generators from A are explicitly given in T, and the defining…

Let ${T_1,...,T_l}$ be a collection of differential operators with constant coefficients on the torus $\mathbb{T}^n$. Consider the Banach space $X$ of functions $f$ on the torus for which all functions $T_j f$, $j=1,...,l$, are continuous.…

We consider the class of autonomous systems $\dot x=f(x)$, where $x \in {\bf R}^{2n}$, $f \in C^1({\bf R}^{2n})$ whose phase portrait is a Cartesian product of $n$ two-dimensional {\em centres}. We also consider perturbations of this…

Let $\varphi:F_1\to F_2$ be an injective morphism of free groups. If $\varphi$ is geometric (i.e. induced by an inclusion of oriented compact connected surfaces with nonempty boundary), then we show that $\varphi$ is an isometric embedding…

Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$), ${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an $F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We fix a Haar…

A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We…

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with…