Related papers: The equivariant coarse Novikov conjecture and coar…

The Nevo-Zimmer theorem classifies the possible intermediate $G$-factors $Y$ in $X \times G/P \to Y \to X$, where $G$ is a higher rank semisimple Lie group, $P$ a minimal parabolic and $X$ an irreducible $G$-space with an invariant…

Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Suppose $\mathcal{X}_G$ has dimension $n$ and it has no factor isometric to either $\mathbb{H}^2$ or…

Let $\S$ be a commutative semigroup with identity $e$ and let $\Gamma$ be a compact subset in the pointwise convergence topology of the space $\S'$ of all non-zero multiplicative functions on $\S.$ Given a continuous function $F: \Gamma \to…

We associate to every $G$-bornological coarse space $X$ and every left-exact $\infty$-category with $G$-action a left-exact infinity-category of equivariant $X$-controlled objects. Postcomposing with algebraic K-theory leads to {new}…

For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…

We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports…

This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…

Consider a proper, isometric action by a unimodular, locally compact group $G$ on a complete Riemannian manifold $M$. For equivariant elliptic operators that are invertible outside a cocompact subset of $M$, we show that a localised index…

The McKay Conjecture (MC) asserts the existence of a bijection between the (inequivalent) complex irreducible representations of degree coprime to $p$ ($p$ a prime) of a finite group $G$ and those of the subgroup $N$, the normalizer of…

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of…

This short note shows how the Novikov conjecture for mapping class groups follows from a theorem of Kato and a result theorem of Hamenstadt.

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite…

We present a formulation of the generalised uncertainty principle based on commutator $\left[ {\hat x}^i, {\hat p}_j \right]$ between position and momentum operators defined in a covariant manner using normal coordinates. We show how any…

A Gauss equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature less than or equal to A, defined by a cubic inequality on the difference of arc and chord, has…

An analogue of the convergence part of the Khintchine-Groshev theorem, as well as its multiplicative version, is proved for nondegenerate smooth submanifolds in $\mathbb{R}^n$. The proof combines methods from metric number theory with a new…

The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the standard complex structure in the complex Euclidean space. In this paper, we consider two natural generalizations of the…

Using computations in the bidual of $\mathbb{B}(L^2M)$ we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of…

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational…

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence…

Let $\lambda$ be a large enough cardinal number (assuming GCH it suffices to let $\lambda=\aleph_\omega$). If $X$ is a Banach space with $\text{dens}(X)\ge\lambda$, which admits a coarse (or uniform) embedding into any $c_0(\Gamma)$, then…