1,995 research outputs found
An explicit KO-degree map and applications
The goal of this note is to study the analog in unstable -homotopy theory of the unit map from the motivic sphere spectrum to the
Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We
show that "Suslin matrices", which are explicit maps from odd dimensional split
smooth affine quadrics to geometric models of the spaces appearing in Bott
periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit
map. As applications, we deduce that for ,
which can be thought of as an extension of Matsumoto's celebrated theorem
describing of a field. These results provide the first step in a program
aimed at computing the sheaf for .Comment: 36 Pages, Final version, to appear Journal of Topolog
F-theory on singular spaces
We propose a framework for treating F-theory directly, without resolving or
deforming its singularities. This allows us to explore new sectors of gauge
theories, including exotic bound states such as T-branes, in a global context.
We use the mathematical framework known as Eisenbud's matrix factorizations for
hypersurface singularities. We display the usefulness of this technique by way
of examples, including affine singularities of both conifold and orbifold type,
as well as a class of full-fledged compact elliptically fibered Calabi-Yau
fourfolds.Comment: 35 pages, 4 figures, minor revision
kk-Theory for Banach Algebras I: The Non-Equivariant Case
kk is a bivariant K-theory for Banach algebras that has
reasonable homological properties, a product and is Morita invariant in a very
general sense. We define it here by a universal property and ensure its
existence in a rather abstract manner using triangulated categories. The
definition ensures that there is a natural transformation from Lafforgue's
theory KK into it so that one can take products of elements in
KK that lie in kk.Comment: 43 page
A new proof for the decidability of D0L ultimate periodicity
We give a new proof for the decidability of the D0L ultimate periodicity
problem based on the decidability of p-periodicity of morphic words adapted to
the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Decidability of the HD0L ultimate periodicity problem
In this paper we prove the decidability of the HD0L ultimate periodicity
problem
Universal cycles and homological invariants of locally convex algebras
Using an appropriate notion of locally convex Kasparov modules, we show how
to induce isomorphisms under a large class of functors on the category of
locally convex algebras; examples are obtained from spectral triples. Our
considerations are based on the action of algebraic K-theory on these functors,
and involve compatibility properties of the induction process with this action,
and with Kasparov-type products. This is based on an appropriate interpretation
of the Connes-Skandalis connection formalism. As an application, we prove Bott
periodicity and a Thom isomorphism for algebras of Schwartz functions
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