# Questions tagged [rigidity]

The tag has no usage guidance.

8 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
633 views

### Definition of a uniformly bounded dual of a group

The unitary dual of a group $G$ is the set of equivalence classes of irreducible unitary representations of $G$ with the Fell topology. (This topology is defined using convergence of positive definite ...
160 views

### How to correctly state Cauchy's rigidity theorem?

Cauchy's rigidity theorem is usually cites briefly as Any two (convex, 3-dimensional) polyhedra with pairwise congruent faces are themselves congruent. As a more formal generalization to general ...
$\newcommand{\M}{\mathcal{M}}$ $\newcommand{\N}{\mathcal{N}}$ $\newcommand{\R}{\mathbb{R}}$ $\newcommand{\CO}[1]{\text{CO}(#1)}$ $\newcommand{\dist}{\operatorname{dist}}$ $\newcommand{\g}{\mathfrak{g}}... 0answers 146 views ### Rigidity vs Super-rigidity of representations (of Kähler/surface groups) In the literature there are several definitions of "rigidity" (or "super-rigidity") of representations, adapted to the circumastances. I wonder what are the relations between them; I excuse in advance ... 0answers 94 views ###$l$-adic rigidity for Milnor$K$-theory Given a local henselian ring$A$with the maximal ideal$m$, does the quotient map$A\mapsto A/m$induce isomorphisms on$l$-adic Milnor$K$-theories? ($K_n^M(R)\otimes \mathbb{Z}_l$, where$l$is an ... 0answers 54 views ### Infinitesimal rigidity vs local rigidity of isometrically immersed riemannian manifolds I was reading the nice survey on rigidity, focusing on tensegrities by Connelly, and I'd like to know the status and feedback about a question he asks: A theorem by Gluck and this work of Connelly, ... 0answers 72 views ### Are a map with constant singular values and its inverse always conjugate through isometries? Let$U \subseteq \mathbb R^2$be open, connected and bounded, and let$0<\sigma_1<\sigma_2$satisfy$\sigma_1 \sigma_2=1$. Suppose that$f:U \to U$is a diffeomorphism whose singular values (of$...
Let $T_a:x\mapsto x+a$ be a Diophantine translation on the torus $\mathbb T^d$, $d>1$. Let $h$ be some $C^1$ diffeomorphism of $\mathbb T^d$ such that $$g=h\circ T_a\circ h^{-1}$$ is $C^\infty$. ...