279 research outputs found
The extended Bloch group and algebraic K-theory
We define an extended Bloch group for an arbitrary field F, and show that
this group is canonically isomorphic to K_3^ind(F) if F is a number field. This
gives an explicit description of K_3^ind(F) in terms of generators and
relations. We give a concrete formula for the regulator, and derive concrete
symbol expressions generating the torsion. As an application, we show that a
hyperbolic 3-manifold with finite volume and invariant trace field k has a
fundamental class in K_3^ind(k) tensor Z[1/2].Comment: 32 pages, 5 figure
A Minimal Poset Resolution of Stable Ideals
We use the theory of poset resolutions to construct the minimal free
resolution of an arbitrary stable monomial ideal in the polynomial ring whose
coefficients are from a field. This resolution is recovered by utilizing a
poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. The
structure of the poset under consideration is quite rich and in related
analysis, we exhibit a regular CW complex which supports a minimal cellular
resolution of a stable monomial ideal.Comment: 25 pages, 2 figure
Various L2-signatures and a topological L2-signature theorem
For a normal covering over a closed oriented topological manifold we give a
proof of the L2-signature theorem with twisted coefficients, using Lipschitz
structures and the Lipschitz signature operator introduced by Teleman. We also
prove that the L-theory isomorphism conjecture as well as the C^*_max-version
of the Baum-Connes conjecture imply the L2-signature theorem for a normal
covering over a Poincar space, provided that the group of deck transformations
is torsion-free. We discuss the various possible definitions of L2-signatures
(using the signature operator, using the cap product of differential forms,
using a cap product in cellular L2-cohomology,...) in this situation, and prove
that they all coincide.Comment: comma in metadata (author field) added
Laplacians of Covering Complexes
The Laplace operator on a simplicial complex encodes information about the adjacencies between simplices. A relationship between simplicial complexes does not always translate to a relationship between their Laplacians. In this paper we look at the case of covering complexes. A covering of a simplicial complex is built from many copies of simplices of the original complex, maintaining the adjacency relationships between simplices. We show that for dimension at least one, the Laplacian spectrum of a simplicial complex is contained inside the Laplacian spectrum of any of its covering complexes
On computing Belyi maps
We survey methods to compute three-point branched covers of the projective
line, also known as Belyi maps. These methods include a direct approach,
involving the solution of a system of polynomial equations, as well as complex
analytic methods, modular forms methods, and p-adic methods. Along the way, we
pose several questions and provide numerous examples.Comment: 57 pages, 3 figures, extensive bibliography; English and French
abstract; revised according to referee's suggestion
A note on quasi-robust cycle bases
We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n _> 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs
The local Laplace transform of an elementary irregular meromorphic connection
We give a definition of the topological local Laplace transformation for a
Stokes-filtered local system on the complex affine line and we compute in a
topological way the Stokes data of the Laplace transform of a differential
system of elementary type.Comment: 56 pages, 21 figures. V2: Final version to appear in Rend. Sem. Mat.
Univ. Padov
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