897 research outputs found
Operations on integral lifts of K(n)
This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence
that operations on lifts of the functors K(n) to cohomology theories with
values in modules over valuation rings of local number fields, indexed by
Lubin-Tate groups of such fields, are extensions of the groups of automorphisms
of the indexing group laws, by the exterior algebras on the normal bundle to
the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the
2015 Nagoya conference honoring T Ohkawa. Comments very welcome
Annual Survey of Virginia Law: Employment Law
This survey covers legislative and judicial developments in Virginia employment law between June 1986 and June 1987. It does not address the workers\u27 compensation and unemployment compensation statutes but focuses on state labor and fair employment laws and the employment-at-will doctrine
From simplicial Chern-Simons theory to the shadow invariant II
This is the second of a series of papers in which we introduce and study a
rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral
for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected
compact structure groups G. More precisely, we introduce, for general links L
in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson
loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson
(Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then
evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement
with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad
The -genus and a regularization of an -equivariant Euler class
We show that a new multiplicative genus, in the sense of Hirzebruch, can be
obtained by generalizing a calculation due to Atiyah and Witten. We introduce
this as the -genus, compute its value for some examples and
highlight some of its interesting properties. We also indicate a connection
with the study of multiple zeta values, which gives an algebraic interpretation
for our proposed regularization procedure.Comment: 14 pages; version to appear in J. Phys.
Mixable Shuffles, Quasi-shuffles and Hopf Algebras
The quasi-shuffle product and mixable shuffle product are both
generalizations of the shuffle product and have both been studied quite
extensively recently. We relate these two generalizations and realize
quasi-shuffle product algebras as subalgebras of mixable shuffle product
algebras. As an application, we obtain Hopf algebra structures in free
Rota-Baxter algebras.Comment: 14 pages, no figure, references update
Nature of singularities in anisotropic string cosmology
We study nature of singularities in anisotropic string-inspired cosmological
models in the presence of a Gauss-Bonnet term. We analyze two string gravity
models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I
background without an axion field. In both scenarios singularities can be
classified in two ways- the determinant singularity where the main determinant
of the system vanishes and the ordinary singularity where at least one of the
anisotropic expansion rates of the Universe diverges. In the dilaton case,
either of these singularities inevitably appears during the evolution of the
system. In the modulus case, nonsingular cosmological solutions exist both in
asymptotic past and future with determinant and D=2, respectively.
In both scenarios nonsingular trajectories in either future or past typically
meet the determinant singularity in past/future when the solutions are
singular, apart from the exceptional case where the sign of the time-derivative
of dilaton is negative. This implies that the determinant singularity may play
a crucial role to lead to singular solutions in an anisotropic background.Comment: 21 pages, 8 figure
Group entropies, correlation laws and zeta functions
The notion of group entropy is proposed. It enables to unify and generalize
many different definitions of entropy known in the literature, as those of
Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals
are presented, related to nontrivial correlation laws characterizing
universality classes of systems out of equilibrium, when the dynamics is weakly
chaotic. The associated thermostatistics are discussed. The mathematical
structure underlying our construction is that of formal group theory, which
provides the general structure of the correlations among particles and dictates
the associated entropic functionals. As an example of application, the role of
group entropies in information theory is illustrated and generalizations of the
Kullback-Leibler divergence are proposed. A new connection between statistical
mechanics and zeta functions is established. In particular, Tsallis entropy is
related to the classical Riemann zeta function.Comment: to appear in Physical Review
Study of a Class of Four Dimensional Nonsingular Cosmological Bounces
We study a novel class of nonsingular time-symmetric cosmological bounces. In
this class of four dimensional models the bounce is induced by a perfect fluid
with a negative energy density. Metric perturbations are solved in an analytic
way all through the bounce. The conditions for generating a scale invariant
spectrum of tensor and scalar metric perturbations are discussed.Comment: 16 pages, 10 figure
Parametric amplification of metric fluctuations through a bouncing phase
We clarify the properties of the behavior of classical cosmological
perturbations when the Universe experiences a bounce. This is done in the
simplest possible case for which gravity is described by general relativity and
the matter content has a single component, namely a scalar field in a closed
geometry. We show in particular that the spectrum of scalar perturbations can
be affected by the bounce in a way that may depend on the wave number, even in
the large scale limit. This may have important implications for string
motivated models of the early Universe.Comment: 17 pages, 12 figures, LaTeX-ReVTeX format, version to match Phys.
Rev.
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