Endomorphisms of Stable Planes

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Endomorphisms of stable continuous-trace C-algebras

We classify spectrum-preserving endomorphisms of stable continuoustrace C∗-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Phillips and Raeburn. 2000 Mathematics Subject Classification: 46L05, 46M20

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

Topics in Absolute Anabelian Geometry Ii: Decomposition Groups and Endomorphisms

The present paper, which forms the second part of a three-part series in which we study absolute anabelian geometry from an algorithmic point of view, focuses on the study of the closely related notions of decomposition groups and endomorphisms in this anabelian context. We begin by studying an abstract combinatorial analogue of the algebro-geometric notion of a stable polycurve [i.e., a “succe...

VIRTUAL PERMUTATIONS OF Z[Zn] COMPLEXES

We extend the characterization of virtual permutation endomorphisms in the case where IIi(Ai) = Zn. We show that for endomorphisms of Z[Zn] complexes the appropriate eigenvalue condition is that all eigenvalues be roots of units of the group ring Z[Zn\. Among these endomorphisms the virtual permutations are detected by Kq. The main application is in identifying Morse-Smale isotopy classes on th...