Related papers: Continuous homomorphisms on piecewise absolutely c…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
Assume that $M$ is a c.t.m. of $ZFC+CH$ containing a simplified $(\omega_1,2)$-morass, $P\in M$ is the poset adding $\aleph_3$ generic reals and $G$ is $P$-generic over $M$. In $M$ we construct a function between sets of terms in the…
An arbitrary homomorphism between groups is nonincreasing for stable commutator length, and there are infinitely many (injective) homomorphisms between free groups which strictly decrease the stable commutator length of some elements.…
In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian…
We define and develop a homotopy invariant notion for the sequential topological complexity of a map $f:X\to Y,$ denoted $TC_{r}(f)$, that interacts with $TC_{r}(X)$ and $TC_{r}(Y)$ in the same way Jamie Scott's topological complexity map…
Let $S$ be a set of transpositions such that the girth of the transposition graph of $S$ is at least 5. It is shown that the automorphism group of the Cayley graph of the permutation group $H$ generated by $S$ is the semidirect product…
We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…
Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0, 1]$, or $S^1$, and let $\Homeo_+(M)$ (resp. $\Diff_+^1(M)$) be the group of orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It is a…
This paper investigates and classifies a specific class of one-parameter continuous fields of C*-algebras, which can be seen as generalized AI-algebras. Building on the classification of *-homomorphisms between interval algebras by the…
A digraph is connected-homogeneous if every isomorphism between two finite connected induced subdigraphs extends to an automorphism of the whole digraph. In this paper, we completely classify the countable connected-homogeneous digraphs.
It is an open problem whether every continuous homomorphism between infinite-dimensional Lie groups is smooth. In this article, we show that every Hoelder continuous homomorphism is smooth.
An infinite linearly ordered set (S,<=) is called doubly homogeneous if its automorphism group A(S) acts 2-transitively on it. We show that any group G arises as outer automorphism group G cong Out(A(S)) of the automorphism group A(S), for…
We prove that AF-embeddability is a homotopy invariant in the class of separable exact $C^*$-algebras. This work was inspired by Spielberg's work on homotopy invariance of AF-embeddability and Dadarlat's serial works on AF-embeddability of…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…
We consider generalized interval exchange transformations, or briefly GIETs, that is bijections of the interval which are piecewise increasing homeomorphisms with finite branches. When all continuous branches are translations, such maps are…
Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…
Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…
Let $I=[0,1)$ and $\mathcal{PC}(I)$ [resp. $\mathcal{PC}^+(I)$] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preserving] bijections of $I$ by its normal subgroup consisting in…