20,194 research outputs found
Another approach to topological descent theory
In the category Top of topological spaces and continuous functions, we prove that descent
morphisms with respect to the class IE of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations IE(X) of the
basic fibration given by Top/X which are, essentially, complete lattices. Also effective descent
morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes IE satisfying suitable conditions, we show that the class of effective descent
morphisms coincides with the one of effective IE-descent morphisms.CMUC/FCT PRAXIS Projects 2/2.1/MAT/46/94, PCEX/P/MAT/46/9
Another Approach to Topological Descent Theory
In the category Top of topological spaces and continuous functions, we prove that surjective maps which are descent morphisms with respect to the class E of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations E(X) of the basic fibration given by Top/X which are, essentially, complete lattices. Also effective descent morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes E satisfying suitable conditions, we show that the class of effective descent morphisms coincides with the one of effective E-descent morphisms
Quantum Field Theory and Differential Geometry
We introduce the historical development and physical idea behind topological
Yang-Mills theory and explain how a physical framework describing subatomic
physics can be used as a tool to study differential geometry. Further, we
emphasize that this phenomenon demonstrates that the interrelation between
physics and mathematics have come into a new stage.Comment: 29 pages, enlarged version, some typewritten mistakes have been
corrected, the geometric descrition to BRST symmetry, the chain of descent
equations and its application in TYM as well as an introduction to R-symmetry
have been added, as required by mathematicia
Anomaly Inflow and Membrane Dynamics in the QCD Vacuum
Large and holographic arguments, as well as Monte Carlo results,
suggest that the topological structure of the QCD vacuum is dominated by
codimension-one membranes which appear as thin dipole layers of topological
charge. Such membranes arise naturally as branes in the holographic
formulation of QCD based on IIA string theory. The polarizability of these
membranes leads to a vacuum energy , providing the origin of
nonzero topological susceptibility. Here we show that the axial U(1) anomaly
can be formulated as anomaly inflow on the brane surfaces. A 4D gauge
transformation at the brane surface separates into a 3D gauge transformation of
components within the brane and the transformation of the transverse component.
The in-brane gauge transformation induces currents of an effective Chern-Simons
theory on the brane surface, while the transformation of the transverse
component describes the transverse motion of the brane and is related to the
Ramond-Ramond closed string field in the holographic formulation of QCD. The
relation between the surface currents and the transverse motion of the brane is
dictated by the descent equations of Yang-Mills theory.Comment: 22 pages, 3 figure
Observables in Topological Yang-Mills Theories
Using topological Yang-Mills theory as example, we discuss the definition and
determination of observables in topological field theories (of Witten-type)
within the superspace formulation proposed by Horne. This approach to the
equivariant cohomology leads to a set of bi-descent equations involving the
BRST and supersymmetry operators as well as the exterior derivative. This
allows us to determine superspace expressions for all observables, and thereby
to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type
gauge.Comment: 39 pages, Late
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