Royden algebras and quasi-isometries of Riemannian manifolds

Quasi-isometries preserve the geometric decomposition of Haken manifolds

We prove quasi-isometry invariance of the canonical decomposition for fundamental groups of Haken 3-manifolds with zero Euler characteristic. We show that groups quasi-isometric to Haken manifold groups with nontrivial canonical decomposition are finite extensions of Haken orbifold groups. As a by-product we describe all 2-dimensional quasi-flats in the universal covers of non-geometric Haken m...

Meromorphic open-string vertex algebras and Riemannian manifolds

Let M be a Riemannian manifold. For p ∈ M , the tensor algebra of the negative part of the (complex) affinization of the tangent space of M at p has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over M with a connection. We construct a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel...

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

MATHEMA TICS: S. B. MYERS ISOMETRIES OF 2-DIMENSIONAL RIEMANNIAN MANIFOLDS INTO THEMSELVES By SUMNER

Isometries Between Matrix Algebras

As an attempt to understand linear isometries between C∗-algebras without the surjectivity assumption, we study linear isometries between matrix algebras. Denote by Mm the algebra of m×m complex matrices. If k ≥ n and φ : Mn → Mk has the form X 7→ U [X ⊕ f(X)]V or X 7→ U [X t ⊕ f(X)]V for some unitary U, V ∈ Mk and contractive linear map f : Mn → Mk, then ‖φ(X)‖ = ‖X‖ for all X ∈ Mn. We prove t...