3,377 research outputs found
Homology and Bisimulation of Asynchronous Transition Systems and Petri Nets
Homology groups of labelled asynchronous transition systems and Petri nets
are introduced. Examples of computing the homology groups are given. It is
proved that if labelled asynchronous transition systems are bisimulation
equivalent, then they have isomorphic homology groups. A method of constructing
a Petri net with given homology groups is found.Comment: 21 page
Loop groups and noncommutative geometry
We describe the representation theory of loop groups in terms of K-theory and
noncommutative geometry. This is done by constructing suitable spectral triples
associated with the level l projective unitary positive-energy representations
of any given loop group . The construction is based on certain
supersymmetric conformal field theory models associated with LG in the setting
of conformal nets. We then generalize the construction to many other rational
chiral conformal field theory models including coset models and the moonshine
conformal net.Comment: Revised versio
The K-homology of nets of C*-algebras
Let X be a space, intended as a possibly curved spacetime, and A a precosheaf
of C*-algebras on X. Motivated by algebraic quantum field theory, we study the
Kasparov and Theta-summable K-homology of A interpreting them in terms of the
holonomy equivariant K-homology of the associated C*-dynamical system. This
yields a characteristic class for K-homology cycles of A with values in the odd
cohomology of X, that we interpret as a generalized statistical dimension.Comment: To appear in Journal of Geometry and Physic
Resonant bands, Aomoto complex, and real 4-nets
The resonant band is a useful notion for the computation of the nontrivial
monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this
article, we develop the resonant band description for the cohomology of the
Aomoto complex. As an application, we prove that real 4-nets do not exist.Comment: 23 pages, 7 figure
Quantization of Whitney functions
We propose to study deformation quantizations of Whitney functions. To this
end, we extend the notion of a deformation quantization to algebras of Whitney
functions over a singular set, and show the existence of a deformation
quantization of Whitney functions over a closed subset of a symplectic
manifold. Under the assumption that the underlying symplectic manifold is
analytic and the singular subset subanalytic, we determine that the Hochschild
and cyclic homology of the deformed algebra of Whitney functions over the
subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we
note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page
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