Equivariance of generalized Chern characters
نویسنده
چکیده
In this note some generalization of the Chern character is discussed from the chromatic point of view. We construct a multiplicative Gn+1-equivariant natural transformation Θ from some height n + 1 cohomology theory E∗(−) to the height n cohomology theory K∗(−)b ⊗FL, where K∗(−) is essentially the nth Morava K-theory. As a corollary, it is shown that the Gn-module K ∗(X) can be recovered from the Gn+1-module E ∗(X). We also construct a lift of Θ to a natural transformation between characteristic zero cohomology theories.
منابع مشابه
Geometry of Generalized Coherent States : Some Calculations of Chern Characters
This is a continuation of the preceding paper (hep–ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of some bundle. Next for a set of generalized coherent states we define a universal bundle over the infinite–dimensional Grassmann manifold and construct the pu...
متن کاملAction of Automorphisms on Irreducible Characters of Symplectic Groups
Assume G is a finite symplectic group Sp2n(q) over a finite field Fq of odd characteristic. We describe the action of the automorphism group Aut(G) on the set Irr(G) of ordinary irreducible characters of G. This description relies on the equivariance of Deligne–Lusztig induction with respect to automorphisms. We state a version of this equivariance which gives a precise way to compute the autom...
متن کاملFlux quantization and the M-theoretic characters
In a previous work [1] we introduced characters and classes built out of the M-theory four-form and the Pontrjagin classes, which we used to express the Chern-Simons and the one-loop terms in a way that makes the topological structures behind them more transparent. In this paper we further investigate such classes and the corresponding candidate generalized cohomology theories. In particular, w...
متن کاملGeometry of Coherent States : Some Examples of Calculations of Chern–Characters
First we make a brief review of coherent states and prove that the resolution of unity can be obtained by the 1–st Chern character of some bundle. Next we define a Grassmann manifold for a set of coherent states and construct the pull–back bundle making use of a projector from the parameter space to this Grassmann manifold. We study some geometric properties (Chern–characters mainly) of these b...
متن کاملSome Index Formulæ on the Moduli Space of Stable Parabolic Vector Bundles
We study natural families of ∂-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulæ for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabo...
متن کامل