170 research outputs found
Classification and Characterization of rationally elliptic manifolds in low dimensions
We give a characterization of closed, simply connected, rationally elliptic
6-manifolds in terms of their rational cohomology rings and a partial
classification of their real cohomology rings. We classify rational, real and
complex homotopy types of closed, simply connected, rationally elliptic
7-manifolds. We give partial results in dimensions 8 and 9.Comment: 23 pages; extended Section 2, revised Section 5 and several minor
revision
Support Varieties and Representation Type of Self-Injective Algebras
We use the theory of varieties for modules arising from Hochschild cohomology
to give an alternative version of the wildness criterion of Bergh and Solberg:
If a finite dimensional self-injective algebra has a module of complexity at
least 3 and satisfies some finiteness assumptions on Hochschild cohomology,
then the algebra is wild. We show directly how this is related to the analogous
theory for Hopf algebras that we developed. We give applications to many
different types of algebras: Hecke algebras, reduced universal enveloping
algebras, small half-quantum groups, and Nichols (quantum symmetric) algebras.Comment: 21 page
Loop operators and S-duality from curves on Riemann surfaces
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples.Comment: 41 page
No time machines in classical general relativity
Irrespective of local conditions imposed on the metric, any extendible
spacetime U has a maximal extension containing no closed causal curves outside
the chronological past of U. We prove this fact and interpret it as
impossibility (in classical general relativity) of the time machines, insofar
as the latter are defined to be causality-violating regions created by human
beings (as opposed to those appearing spontaneously).Comment: A corrigendum (to be published in CQG) has been added to correct an
important mistake in the definition of localit
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