1,454 research outputs found
Classifying spaces for commutativity of low-dimensional Lie groups
For each of the groups , we compute the integral and
-cohomology rings of (the classifying space for
commutativity of ), the action of the Steenrod algebra on the mod 2
cohomology, the homotopy type of (the homotopy fiber of the
inclusion ), and some low-dimensional homotopy groups of
.Comment: A shortened version, without the appendices, has been accepted in
Math. Proc. Camb. Philos. So
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
We use noncommutative topology to study T-duality for principal torus bundles
with H-flux. We characterize precisely when there is a "classical" T-dual,
i.e., a dual bundle with dual H-flux, and when the T-dual must be
"non-classical," that is, a continuous field of noncommutative tori.
The duality comes with an isomorphism of twisted -theories, required for
matching of D-brane charges, just as in the classical case. The isomorphism of
twisted cohomology which one gets in the classical case is replaced in the
non-classical case by an isomorphism of twisted cyclic homology.
An important part of the paper contains a detailed analysis of the
classifying space for topological T-duality, as well as the T-duality group and
its action. The issue of possible non-uniqueness of T-duals can be studied via
the action of the T-duality group.Comment: Latex2e, 36 pages, 2 figures, uses xypic, few minor changes mad
Niceness theorems
Many things in mathematics seem lamost unreasonably nice. This includes
objects, counterexamples, proofs. In this preprint I discuss many examples of
this phenomenon with emphasis on the ring of polynomials in a countably
infinite number of variables in its many incarnations such as the representing
object of the Witt vectors, the direct sum of the rings of representations of
the symmetric groups, the free lambda ring on one generator, the homology and
cohomology of the classifying space BU, ... . In addition attention is paid to
the phenomenon that solutions to universal problems (adjoint functors) tend to
pick up extra structure.Comment: 52 page
Excision for deformation K-theory of free products
Associated to a discrete group , one has the topological category of
finite dimensional (unitary) -representations and (unitary) isomorphisms.
Block sums provide this category with a permutative structure, and the
associated -theory spectrum is Carlsson's deformation -theory of G. The
goal of this paper is to examine the behavior of this functor on free products.
Our main theorem shows the square of spectra associated to (considered as
an amalgamated product over the trivial group) is homotopy cartesian. The proof
uses a general result regarding group completions of homotopy commutative
topological monoids, which may be of some independent interest.Comment: 32 pages, 1 figure. Final version: The title has changed, and the
paper has been substantially revised to improve clarit
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