4,274 research outputs found
Realising formal groups
We show that a large class of formal groups can be realised functorially by
even periodic ring spectra. The main advance is in the construction of
morphisms, not of objects.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-8.abs.htm
Gross-Hopkins duality
We give a new and simpler proof of a result of Hopkins and Gross relating
Brown-Comenetz duality to Spanier-Whitehead duality in the K(n)-local stable
homotopy category
Morava E-theory of symmetric groups
We compute the completed E(n) cohomology of the classifying spaces of the
symmetric groups, and relate the answer to the theory of finite subgroups of
formal groups.Comment: To appear in Topolog
Common subbundles and intersections of divisors
Let V_0 and V_1 be complex vector bundles over a space X. We use the theory
of divisors on formal groups to give obstructions in generalised cohomology
that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that
V_0\cap V_1 has dimension at least k everywhere. We study various algebraic
universal examples related to this question, and show that they arise from the
generalised cohomology of corresponding topological universal examples. This
extends and reinterprets earlier work on degeneracy classes in ordinary
cohomology or intersection theory.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-42.abs.htm
The Hopf Rings for KO and KU
We compute the mod two homology Hopf rings of the spectra KO and KU. The
spaces in these spectra are the infinite classical groups and their coset
spaces, and their homology was first calculated in the Cartan seminars, but the
Hopf ring structure was first determined in the second author's unpublished PhD
thesis. The presentation given here serves as an introduction to the first
author's much more intricate work on the connective spectrum bo. The Hopf ring
viewpoint turns out to be very convenient for understanding the homological
effect of various maps between classical groups and fibrations of their
connective covers.Comment: 20 pages; to appear in JPA
Thermalization and the chromo-Weibel instability
Despite the apparent success of ideal hydrodynamics in describing the
elliptic flow data which have been produced at Brookhaven National Lab's
Relativistic Heavy Ion Collider, one lingering question remains: is the use of
ideal hydrodynamics at times t < 1 fm/c justified? In order to justify its use
a method for rapidly producing isotropic thermal matter at RHIC energies is
required. One of the chief obstacles to early isotropization/thermalization is
the rapid longitudinal expansion of the matter during the earliest times after
the initial nuclear impact. As a result of this expansion the parton
distribution functions become locally anisotropic in momentum space. In
contrast to locally isotropic plasmas anisotropic plasmas have a spectrum of
soft unstable modes which are characterized by exponential growth of transverse
chromo-magnetic/-electric fields at short times. This instability is the QCD
analogue of the Weibel instability of QED. Parametrically the chromo-Weibel
instability provides the fastest method for generation of soft background
fields and dominates the short-time dynamics of the system.Comment: 8 pages, 4 figures, Invited plenary talk given at the 19th
International Conference on Ultrarelativistic Nucleus-Nucleus Collisions:
Quark Matter 2006 (QM 2006), Shanghai, China, 14-20 Nov 200
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