22 research outputs found
Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds
For an oriented finite volume hyperbolic 3-manifold M with a fixed spin
structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly
speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to
the representation given by the composition of the lift of the holonomy
representation defined by \eta, and the n-dimensional, irreducible, complex
representation of SL(2,C). In the present work, we focus on two aspects of this
invariant: its asymptotic behavior and its relationship with the complex-length
spectrum of the manifold. Concerning the former, we prove that for suitable
spin structures, log(\tau_n(M; \eta)) grows as -n^2 Vol(M)/4\pi, extending thus
the result obtained by W. Mueller for the compact case. Concerning the latter,
we prove that the sequence {\tau_n(M; \eta)} determines the complex-length
spectrum of the manifold up to complex conjugation
Nonstable K-Theory for graph algebras
We compute the monoid V (LK(E)) of isomorphism classes of finitely generated
projective modules over certain graph algebras LK(E), and we show that this monoid satisfies
the refinement property and separative cancellation. We also show that there is a natural
isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals
of V (LK(E)). When K is the field C of complex numbers, the algebra LC(E) is a dense
subalgebra of the graph C -algebra C (E), and we show that the inclusion map induces an
isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra
of any row-finite graph turns out to satisfy the stable weak cancellation propert