85 research outputs found
Uniform Local Amenability
The main results of this paper show that various coarse (`large scale')
geometric properties are closely related. In particular, we show that property
A implies the operator norm localisation property, and thus that norms of
operators associated to a very large class of metric spaces can be effectively
estimated.
The main tool is a new property called uniform local amenability. This
property is easy to negate, which we use to study some `bad' spaces. We also
generalise and reprove a theorem of Nowak relating amenability and asymptotic
dimension in the quantitative setting
THE CONCENTRATION OF FREE AMINO ACIDS IN BLOOD SERUM OF HEALTHY COWS AND COWS WITH SUBCLINICAL KETOSIS
This paper presents the study on determination of the free amino acid in blood serum of cows with high milk production (Herd A) and cows with subclinical ketosis compared to healthy ones (Herd B). In Herd A examinated 12 cows in the first 100 days in milk. A total of 24 cows from a herd B divided into two groups: experimental (12 cows with ketosis) and control (12 healthy cows) were included in the study. Statistically significantly higher concentrations of glutamine, glutamic acid, isoleucine (p ≤ 0.001), and tyrosine (p ≤ 0.05) were found in dairy cows with subclinical ketosis compared to healthy ones. A significant decrease in the concentrations of asparagine, histidine, methionine, and serine (p ≤ 0.001) as well as alanine, leucine, lysine and proline (p ≤ 0.05) was observed. In Herd A was high level of total essential amino acids in blood serum. In our study, the changes, in particular, observed in amino acid concentration in cows with subclinical ketosis indicate its intensive use in both ketogenesis and gluconeogenesis processes
Cycles in the chamber homology of GL(3)
Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the
existence of parahoric types for GL(N). We construct representative cycles in
all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction
Property A and CAT(0) cube complexes
Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable
D-branes, KK-theory and duality on noncommutative spaces
We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a refinement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies
Spin Foams and Noncommutative Geometry
We extend the formalism of embedded spin networks and spin foams to include
topological data that encode the underlying three-manifold or four-manifold as
a branched cover. These data are expressed as monodromies, in a way similar to
the encoding of the gravitational field via holonomies. We then describe
convolution algebras of spin networks and spin foams, based on the different
ways in which the same topology can be realized as a branched covering via
covering moves, and on possible composition operations on spin foams. We
illustrate the case of the groupoid algebra of the equivalence relation
determined by covering moves and a 2-semigroupoid algebra arising from a
2-category of spin foams with composition operations corresponding to a fibered
product of the branched coverings and the gluing of cobordisms. The spin foam
amplitudes then give rise to dynamical flows on these algebras, and the
existence of low temperature equilibrium states of Gibbs form is related to
questions on the existence of topological invariants of embedded graphs and
embedded two-complexes with given properties. We end by sketching a possible
approach to combining the spin network and spin foam formalism with matter
within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure
Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
We apply some methods of homology and K-theory to special classes of branes
wrapping homologically nontrivial cycles. We treat the classification of
four-geometries in terms of compact stabilizers (by analogy with Thurston's
classification of three-geometries) and derive the K-amenability of Lie groups
associated with locally symmetric spaces listed in this case. More complicated
examples of T-duality and topology change from fluxes are also considered. We
analyse D-branes and fluxes in type II string theory on with torsion flux and demonstrate in details
the conjectured T-duality to with no flux. In the
simple case of , T-dualizing the circles reduces to
duality between with
flux and with no flux.Comment: 27 pages, tex file, no figure
Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
We develop quantization techniques for describing the nonassociative geometry
probed by closed strings in flat non-geometric R-flux backgrounds M. Starting
from a suitable Courant sigma-model on an open membrane with target space M,
regarded as a topological sector of closed string dynamics in R-space, we
derive a twisted Poisson sigma-model on the boundary of the membrane whose
target space is the cotangent bundle T^*M and whose quasi-Poisson structure
coincides with those previously proposed. We argue that from the membrane
perspective the path integral over multivalued closed string fields in Q-space
is equivalent to integrating over open strings in R-space. The corresponding
boundary correlation functions reproduce Kontsevich's deformation quantization
formula for the twisted Poisson manifolds. For constant R-flux, we derive
closed formulas for the corresponding nonassociative star product and its
associator, and compare them with previous proposals for a 3-product of fields
on R-space. We develop various versions of the Seiberg-Witten map which relate
our nonassociative star products to associative ones and add fluctuations to
the R-flux background. We show that the Kontsevich formula coincides with the
star product obtained by quantizing the dual of a Lie 2-algebra via convolution
in an integrating Lie 2-group associated to the T-dual doubled geometry, and
hence clarify the relation to the twisted convolution products for topological
nonassociative torus bundles. We further demonstrate how our approach leads to
a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde
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