相关论文: Non-trivial copies of N*

We study the existence of universal autohomeomorphisms of $\mathbb{N}^*$. We prove that $\mathsf{CH}$ implies there is such an autohomeomorphism and show that there are none in any model where all autohomeomorphisms of $\mathbb{N}^*$ are…

We study the group of automorphisms of certain corona C*-algebras. As a corollary of a more general C*-algebraic result, we show that, under the Continuum Hypothesis, $\beta X\setminus X$ has nontrivial homeomorphisms, whenever $X$ is a…

It is shown to be consistent that there is a non-trivial autohomeomorphism of beta N while all such autohomeomorphisms are trivial on some open set. The model used is one due to Velickovic in which, coincidentally, Martin's Axiom also…

For any $n \geq 3$ and any closed manifold $\mathcal{N}$ with $\pi_{n+k}(\mathcal{N}) \neq \{0\}$ for some $k \geq 0$, we establish the existence of nontrivial $n$-harmonic maps from $\mathbb{S}^n$ into $\mathcal{N}$. When $k\geq 1$, these…

We study conditions on automorphisms of Boolean algebras of the form $P(\lambda)/I_\kappa$ (where $\lambda$ is an uncountable cardinal and $I_\kappa$ is the ideal of sets of cardinality less than $\kappa$) which allow one to conclude that a…

In the study of the Stone-\u{C}ech remainder of the real line a detailed study of the Stone-\u{C}ech remainder of the space $\mathbb N\times [0,1]$, which we denote as $\mathbb M$, has often been utilized. Of course the real line can be…

An n-homomorphism between algebras is a linear map $\phi : A \to B$ such that $\phi(a_1 ... a_n) = \phi(a_1)... \phi(a_n)$ for all elements $a_1, >..., a_n \in A.$ Every homomorphism is an n-homomorphism, for all n >= 2, but the converse is…

Martin's Axiom does not imply that all automorphisms of P(N)/[N]^{<aleph_0} are somewhere trivial.

Generalising a conjecture of Singerman, it is shown that there exist orientably regular chiral hypermaps of every non-spherical type. The proof uses the representation theory of automorphism groups acting on homology and on various spaces…

Every expanding map on a closed manifold is topologically conjugate to an expanding map on an infra-nilmanifold, but not every infra-nilmanifold admits an expanding map. In this article we give a complete algebraic characterization of the…

In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating…

If $\lambda$ is (strongly) inaccessible and $2^\lambda = \lambda^+$, then there is a nowhere trivial automorphism of the Boolean algebra $\mathcal P(\lambda)/[\lambda]^{<\lambda}$.

We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^*$- and $C$-embedding. We show that $\mathbb{R}^{\omega_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^*$-embedded.

A long-standing conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we settle the conjecture for a finite $p$-group ($p >2$) of nilpotency class $n$ with certain conditions.

We show that if $\kappa < \aleph_\omega$ Cohen reals are added to a model of $\mathsf{CH}$, then there are nontrivial automorphisms of $\mathcal P(\omega)/\mathrm{Fin}$ in the extension. Under some further hypotheses on the ground model,…

A point x is a (bow) tie-point of a space X if X setminus {x} can be partitioned into (relatively) clopen sets each with x in its closure. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of betaN setminus N=…

We investigate the statement ``all automorphisms of $\mathcal P(\lambda)/[\lambda]^{<\lambda}$ are trivial''. We show that MA implies the statement for regular uncountable $\lambda<2^{\aleph_0}$; that the statement is false for measurable…

We show that several classes of groups G of PL-homeomorphisms of the real line admit non-trivial homomorphisms from G to the additive group of reals that are fixed by every automorphism of G. The classes of groups enjoying the stated…

We present a complete classification of complex projective surfaces $X$ with nontrivial self-maps (i.e. surjective morphisms $f:X\rightarrow X$ which are not isomorphisms) of any given degree. The starting point of our classification are…

We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…