1,255 research outputs found
Positive scalar curvature on manifolds with fibered singularities
A (compact) manifold with fibered -singularities is a (possibly) singular
pseudomanifold with two strata: an open nonsingular stratum
(a smooth open manifold) and a closed stratum (a closed
manifold of positive codimension), such that a tubular neighborhood of is a fiber bundle with fibers each looking like the cone on a fixed closed
manifold . We discuss what it means for such an with fibered
-singularities to admit an appropriate Riemannian metric of positive scalar
curvature, and we give necessary and sufficient conditions (the necessary
conditions based on suitable versions of index theory, the sufficient
conditions based on surgery methods and homotopy theory) for this to happen
when the singularity type is either or , and and the
boundary of the tubular neighborhood of the singular stratum are simply
connected and carry spin structures. Along the way, we prove some results of
perhaps independent interest, concerning metrics on spin manifolds with
positive "twisted scalar curvature," where the twisting comes from the
curvature of the spin line bundle.Comment: 30 pages, 1 figure. An error was corrected in the statement and proof
of the second main theorem, which is now Theorem 3.1
On mysteriously missing T-duals, H-flux and the T-duality group
A general formula for the topology and H-flux of the T-duals of type II
string theories with H-flux on toroidal compactifications is presented here. It
is known that toroidal compactifications with H-flux do not necessarily have
T-duals which are themselves toroidal compactifications. A big puzzle has been
to explain these mysterious ``missing T-duals'', and our paper presents a
solution to this problem using noncommutative topology. We also analyze the
T-duality group and its action, and illustrate these concepts with examples.Comment: 4 pages, latex2e, Mistake in formula corrected, ref. adde
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