According to a result of one of the authors [7] there are at most a countable number of inequivalent differentiable actions of a compact Lie group on a compact differentiable manifold. The results above show that both the compactness of the manifold and the differentiability of the action are necessary assumptions. In the course of our proof we also prove the following theorem, which is an elem...

In this paper we consider families of Böröczky tilings in hyperbolic space in arbitrary dimension, study some basic properties and classify all possible symmetries. In particular, it is shown that these tilings are non-crystallographic, and that there are uncountably many tilings with a fixed prototile.

Let g be a Kac–Moody Lie algebra. We give an interpretation of Tits’ associated group functor using representation theory of g and we construct a locally compact “Kac–Moody group” G over a finite field k. Using (twin) BN-pairs (G,B,N) and (G,B−, N) for G we show that if k is “sufficiently large”, then the subgroup B− is a non-uniform lattice in G. We have also constructed an uncountably infinit...

Sets with transfinite cardinality can be said to have countably infinite cardinality or uncountably infinite cardinality. The cardinality of the set v is said to be countably infinite if there exists an injection between v and the set of natural numbers. It is represented by the symbol א0, read ”aleph.” An uncountably infinite set has a greater cardinality than that of the set of integers; ther...

We associate to triangulations of infinite type surfaces a flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two can be related by sequence flips. A consequence our results that graphs for have uncountably many connected components.

Abstract We conclude the classification of cohomogeneity one actions on symmetric spaces rank by classifying quaternionic hyperbolic up to orbit equivalence. As a by-product our proof, we produce uncountably many examples inhomogeneous isoparametric families hypersurfaces with constant principal curvatures in spaces.

For every total recursive time bound t, a constant fraction of all compressible (low Kolmogorov complexity) strings is t-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length n is compressible to log n yet t-bounded incompressible below 1 4n− log n; and there are countable infinitely many recursiv...

In [HT11], Horč́ık and Terui show that if a substructural logic enjoys the disjunction property, then its tautology problem is PSPACE-hard. We prove that all substructural logics in the interval between intuitionistic logic and generalized Hájek basic logic have a PSPACE-hard tautology problem, which implies that uncountably many substructural logics lacking the disjunction property have a PSPAC...

Sufficient conditions on a space are given which guarantee that the K-theory ring is an invariant of the adic genus. An immediate consequence of this result about adic genus is that for any positive integer n, the power series ring Z[[x1, . . . , xn]] admits uncountably many pairwise non-isomorphic λ-ring structures.