216 research outputs found
Twisted -theory
Twisted complex -theory can be defined for a space equipped with a
bundle of complex projective spaces, or, equivalently, with a bundle of
C-algebras. Up to equivalence, the twisting corresponds to an element of
. We give a systematic account of the definition and basic
properties of the twisted theory, emphasizing some points where it behaves
differently from ordinary -theory. (We omit, however, its relations to
classical cohomology, which we shall treat in a sequel.) We develop an
equivariant version of the theory for the action of a compact Lie group,
proving that then the twistings are classified by the equivariant cohomology
group . We also consider some basic examples of twisted -theory
classes, related to those appearing in the recent work of
Freed-Hopkins-Teleman.Comment: 49 pages;some minor corrections have been made to the earlier versio
Anyons in Geometric Models of Matter
We show that the "geometric models of matter" approach proposed by the first
author can be used to construct models of anyon quasiparticles with fractional
quantum numbers, using 4-dimensional edge-cone orbifold geometries with
orbifold singularities along embedded 2-dimensional surfaces. The anyon states
arise through the braid representation of surface braids wrapped around the
orbifold singularities, coming from multisections of the orbifold normal bundle
of the embedded surface. We show that the resulting braid representations can
give rise to a universal quantum computer.Comment: 22 pages LaTe
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