227 research outputs found
The Serre spectral sequence of a noncommutative fibration for de Rham cohomology
For differential calculi on noncommutative algebras, we construct a twisted
de Rham cohomology using flat connections on modules. This has properties
similar, in some respects, to sheaf cohomology on topological spaces. We also
discuss generalised mapping properties of these theories, and relations of
these properties to corings. Using this, we give conditions for the Serre
spectral sequence to hold for a noncommutative fibration. This might be better
read as giving the definition of a fibration in noncommutative differential
geometry. We also study the multiplicative structure of such spectral
sequences. Finally we show that some noncommutative homogeneous spaces satisfy
the conditions to be such a fibration, and in the process clarify the
differential structure on these homogeneous spaces. We also give two explicit
examples of differential fibrations: these are built on the quantum Hopf
fibration with two different differential structures.Comment: LaTeX, 33 page
Obturator Artery Aneurysm
AbstractWe present a case of a symptomatic obturator artery aneurysm. The patient was investigated for a possible rectal tumor. The final diagnosis was made during surgery, despite the presence of imaging studies. The operation consisted of simple ligation of inflow and outflow of the aneurysm. Satisfying early and long term result indicates that this is a sufficient operative procedure in such an aneurysm
Quantum teardrops
Algebras of functions on quantum weighted projective spaces are introduced,
and the structure of quantum weighted projective lines or quantum teardrops are
described in detail. In particular the presentation of the coordinate algebra
of the quantum teardrop in terms of generators and relations and classification
of irreducible *-representations are derived. The algebras are then analysed
from the point of view of Hopf-Galois theory or the theory of quantum principal
bundles. Fredholm modules and associated traces are constructed. C*-algebras of
continuous functions on quantum weighted projective lines are described and
their K-groups computed.Comment: 18 page
Canonical quantization of a particle near a black hole
We discuss the quantization of a particle near an extreme Reissner-Nordstrom
black hole in the canonical formalism. This model appears to be described by a
Hamiltonian with no well-defined ground state. This problem can be circumvented
by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF).
We show that the Hamiltonian with no ground state corresponds to a gauge in
which there is an obstruction at the boundary of spacetime requiring a
modification of the quantization rules. The redefinition of the Hamiltonian a
la DFF corresponds to a different choice of gauge. The latter is a good gauge
leading to standard quantization rules. Thus, the DFF trick is a consequence of
a standard gauge-fixing procedure in the case of black hole scattering.Comment: 13 pages, ReVTeX, no figure
Empiric Models of the Earth's Free Core Nutation
Free core nutation (FCN) is the main factor that limits the accuracy of the
modeling of the motion of Earth's rotational axis in the celestial coordinate
system. Several FCN models have been proposed. A comparative analysis is made
of the known models including the model proposed by the author. The use of the
FCN model is shown to substantially increase the accuracy of the modeling of
Earth's rotation. Furthermore, the FCN component extracted from the observed
motion of Earth's rotational axis is an important source for the study of the
shape and rotation of the Earth's core. A comparison of different FCN models
has shown that the proposed model is better than other models if used to
extract the geophysical signal (the amplitude and phase of FCN) from
observational data.Comment: 8 pages, 3 figures; minor update of the journal published versio
Quantization of maximally-charged slowly-moving black holes
We discuss the quantization of a system of slowly-moving extreme
Reissner-Nordstrom black holes. In the near-horizon limit, this system has been
shown to possess an SL(2,R) conformal symmetry. However, the Hamiltonian
appears to have no well-defined ground state. This problem can be circumvented
by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF).
We apply the Faddeev-Popov quantization procedure to show that the Hamiltonian
with no ground state corresponds to a gauge in which there is an obstruction at
the singularities of moduli space requiring a modification of the quantization
rules. The redefinition of the Hamiltonian a la DFF corresponds to a different
choice of gauge. The latter is a good gauge leading to standard quantization
rules. Thus, the DFF trick is a consequence of a standard gauge-fixing
procedure in the case of black hole scattering.Comment: Corrected errors in the gauge-fixing procedur
Four problems regarding representable functors
Let , be two rings, an -coring and the
category of left -comodules. The category of all representable functors is shown to be equivalent to the opposite of the
category . For an -bimodule we give
necessary and sufficient conditions for the induction functor to be: a representable functor, an
equivalence of categories, a separable or a Frobenius functor. The latter
results generalize and unify the classical theorems of Morita for categories of
modules over rings and the more recent theorems obtained by Brezinski,
Caenepeel et al. for categories of comodules over corings.Comment: 16 pages, the second versio
On Iterated Twisted Tensor Products of Algebras
We introduce and study the definition, main properties and applications of
iterated twisted tensor products of algebras, motivated by the problem of
defining a suitable representative for the product of spaces in noncommutative
geometry. We find conditions for constructing an iterated product of three
factors, and prove that they are enough for building an iterated product of any
number of factors. As an example of the geometrical aspects of our
construction, we show how to construct differential forms and involutions on
iterated products starting from the corresponding structures on the factors,
and give some examples of algebras that can be described within our theory. We
prove a certain result (called ``invariance under twisting'') for a twisted
tensor product of two algebras, stating that the twisted tensor product does
not change when we apply certain kind of deformation. Under certain conditions,
this invariance can be iterated, containing as particular cases a number of
independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example
and some references adde
Towards Spinfoam Cosmology
We compute the transition amplitude between coherent quantum-states of
geometry peaked on homogeneous isotropic metrics. We use the holomorphic
representations of loop quantum gravity and the
Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at
first order in the vertex expansion, second order in the graph (multipole)
expansion, and first order in 1/volume. We show that the resulting amplitude is
in the kernel of a differential operator whose classical limit is the canonical
hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an
indication that the dynamics of loop quantum gravity defined by the new vertex
yields the Friedmann equation in the appropriate limit.Comment: 8 page
Pre-torsors and Galois comodules over mixed distributive laws
We study comodule functors for comonads arising from mixed distributive laws.
Their Galois property is reformulated in terms of a (so-called) regular arrow
in Street's bicategory of comonads. Between categories possessing equalizers,
we introduce the notion of a regular adjunction. An equivalence is proven
between the category of pre-torsors over two regular adjunctions
and on one hand, and the category of regular comonad arrows
from some equalizer preserving comonad to on
the other. This generalizes a known relationship between pre-torsors over equal
commutative rings and Galois objects of coalgebras.Developing a bi-Galois
theory of comonads, we show that a pre-torsor over regular adjunctions
determines also a second (equalizer preserving) comonad and a
co-regular comonad arrow from to , such that the
comodule categories of and are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte
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