‎in this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎we also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Let hom-Ln(C) be the algebraic set of complex n-dimensional hom-Lie algebras. The group GL(n,C) acts on it via change basis. We classify structures with nilpotent twisting map 3-dimensional Lie algebras, up to isomorphism, and we give classification orbit closures in such family. For this purpose, introduce some invariants algebras study both problems. ideas techniques presented here can easily...

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

Basics of Elliott’s classification program are outlined and juxtaposed with the abstract classification theory from descriptive set theory. Some preliminary estimates on the complexity of the isomorphism relation of separable C*-algebras are given.

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C. Doche, T. Icart and D. R. Kohel.