1,137 research outputs found
Actions of SL(n,Z) on homology spheres
Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2
homology sphere factors through a finite group action if r < n - 1. In
particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere
factors through a finite group action.Comment: 11 page
Spin polarisation by external magnetic fields, Aharonov-Bohm flux strings, and chiral symmetry breaking in QED
In the first part, the induced vacuum spin around an Aharonov-Bohm flux
string in massless three-dimensional QED is computed explicitly and the result
is shown to agree with a general index theorem. A previous observation in the
literature, that the presence of induced vacuum quantum numbers which are not
periodic in the flux make an integral-flux AB string visible, is reinforced. In
the second part, a recent discussion of chiral symmetry breaking by external
magnetic fields in parity invariant QED and its relation to the induced
spin in parity non-invariant QED is further elaborated. Finally other
vacuum polarisation effects around flux tubes in different variants of QED, in
three and four dimensions are mentioned.Comment: 20 page Latex fil
Simple braids for surface homeomorphisms
Let S be a compact, oriented surface with negative Euler characteristic and
let f be a homeomorphism of S that is isotopic to the identity. If there exists
a periodic orbit with a non-zero rotation vector, then there exists a simple
braid with the same rotation vector.Comment: 12 pages, 2 figure
On 3-manifolds that support partially hyperbolic diffeomorphisms
Let M be a closed 3-manifold that supports a partially hyperbolic
diffeomorphism f. If is nilpotent, the induced action of f on
is partially hyperbolic. If is almost nilpotent or if
has subexponential growth, M is finitely covered by a circle bundle
over the torus. If is almost solvable, M is finitely covered by a
torus bundle over the circle. Furthermore, there exist infinitely many
hyperbolic 3-manifolds that do not support dynamically coherent partially
hyperbolic diffeomorphisms; this list includes the Weeks manifold.
If f is a strong partially hyperbolic diffeomorphism on a closed 3-manifold M
and if is nilpotent, then the lifts of the stable and unstable
foliations are quasi-isometric in the universal of M. It then follows that f is
dynamically coherent.
We also provide a sufficient condition for dynamical coherence in any
dimension. If f is center bunched and if the center-stable and center-unstable
distributions are Lipschitz, then the partially hyperbolic diffeomorphism f
must be dynamically coherent.Comment: 21 page
Monotone periodic orbits for torus homeomorphisms
Let f be a homeomorphism of the torus isotopic to the identity and suppose
that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q),
then f has a topologically monotone periodic orbit with the same rotation
vector.Comment: 10 pages, 1 figur
- …