29,784 research outputs found
Periodicity in the cohomology of symmetric groups via divided powers
A famous theorem of Nakaoka asserts that the cohomology of the symmetric
group stabilizes. The first author generalized this theorem to non-trivial
coefficient systems, in the form of -modules over a field, though
one now obtains periodicity of the cohomology instead of stability. In this
paper, we further refine these results. Our main theorem states that if is
a finitely generated -module over a noetherian ring
then admits the structure of a
-module, where is the divided power algebra over
in a single variable, and moreover, this -module is
"nearly" finitely presented. This immediately recovers the periodicity result
when is a field, but also shows, for example, how the torsion
varies with when . Using the theory of connections
on -modules, we establish sharp bounds on the period in the case
where is a field. We apply our theory to obtain results on the
modular cohomology of Specht modules and the integral cohomology of unordered
configuration spaces of manifolds.Comment: Fixed some minor mistakes and expanded the section on configuration
space
Structural operational semantics for stochastic and weighted transition systems
We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature
Only rational homology spheres admit to be union of DE attractors
If there exists a diffeomorphism on a closed, orientable -manifold
such that the non-wandering set consists of finitely many
orientable attractors derived from expanding maps, then must be a
rational homology sphere; moreover all those attractors are of topological
dimension .
Expanding maps are expanding on (co)homologies.Comment: 23 pages, 2 figure
The Constructive method for query containment checking (extended version)
We present a new method that checks Query Containment for queries with negated derived atoms and/or integrity constraints.
Existing methods for Query Containment checking that deal with these cases do not check actually containment but another
related property called uniform containment, which is a sufficient but not necessary condition for containment. Our method can
be seen as an extension of the canonical databases approach beyond the class of conjunctive queries.Postprint (published version
Discrete orbits, recurrence and solvable subgroups of Diff(C^2,0)
We discuss the local dynamics of a subgroup of Diff(C^2,0) possessing locally
discrete orbits as well as the structure of the recurrent set for more general
groups. It is proved, in particular, that a subgroup of Diff(C^2,0) possessing
locally discrete orbits must be virtually solvable. These results are of
considerable interest in problems concerning integrable systems.Comment: The first version of this paper and "A note on integrability and
finite orbits for subgroups of Diff(C^n,0)" are an expanded version of our
paper "Discrete orbits and special subgroups of Diff(C^n,0)". An intermediate
version re-submitted to the journal on March 2015 is available at
http://www.fep.up.pt/docentes/hreis/publications.htm where there is also a
comparison between these 3 version
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