Cohomology groups of vector-valued forms on symmetric spaces.
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Cohomology groups of vector-valued forms on symmetric spaces. [Lectures delivered at the University of Chicago by] by Shingo Murakami

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Published in [Chicago .
Written in English


  • Vector spaces.,
  • Group theory.,
  • Homology theory.

Book details:

Edition Notes

StatementS. Murakami [during the summer quarter of 1966] Notes prepared by Frank Grosshans.
SeriesUniversity of Chicago mathematics lecture notes, Mathematics lecture notes (University of Chicago. Dept. of Mathematics)
ContributionsGrosshans, Frank D., 1942-
The Physical Object
Pagination140 p.
Number of Pages140
ID Numbers
Open LibraryOL22374228M

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cohomology of finite symmetric groups. groups. For example, there is a subgroup of the form (Z/2) ~ x rat in the Mathieu group M22, with odd index, and the stability conditions to determine the exact image of the restriction map in rood 2 cohomology can be described explicitly (see If X is a space with basepoint, the natural inclusions. For any ring-theory E, the cohomology of symmetric groups L n E (BS n) forms a (derived) Hopf ring where The product is the standard product (with zero products between distinct summands). The coproduct is induced by the standard covering p: BS n BS m!BS n+m. The product is the transfer associated to p. The cohomology of the configuration space of n points in R^3 admits a symmetric group action and has been shown to be isomorphic to the regular : Michael Atiyah. CONSTRUCTION OF COHOMOLOGY OF DISCRETE GROUPS Y. L. TONG AND S. P. WANG ABSTRACT. A correspondence between Hermitian modular forms and vector valued harmonic forms in locally symmetric spaces associated to U(p,q) is constructed and also shown in general to be nonzero. The construction utilizes.

The de Rham theorem states that this mapping is an isomorphism, so that the de Rham and singular cohomology groups with real coefficients are identical for manifolds. This allows us to deduce information about forms from topological properties. Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Draft: March28, Organization vii of dual space and quotient space. Then inSection we will turn to the main topics of this chapter, the concept of -tensor and (the future key ingredient in our exposition of. Complex forms of quaternionic symmetric spaces. Complex, Contact and Symmetric Manifolds A note on the linear cycle space for groups of hermitian type [with R. Zierau]. Journal of Lie Theory, vol. 13 (), pp. Symmetric spaces which are real cohomology spheres. Journal of Differential Geometry, vol. 3 (), pp.

We elaborate one line of proofs for the calculation of homology and cohomology of symmetric groups, through subgroups. We focus on the example of S_4. We start with the elementary fact that the mod-p cohomology of a group injects into the cohomology of its p-Sylow subgroup.   This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character . Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras Cambridge Studies in Advanced Mathematics, ISSN Repr of Ed) Volume 1 of Representations and Cohomology, David J. Benson: Author: D. J. Benson: Edition: reprint, revised: Publisher: Cambridge University Press, ISBN. This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of authors study the cohomology of locally symmetric spaces for GL (N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL (N).