Book Review: Lie groups and compact groups

Lie Groups and p-Compact Groups

A p-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of p-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on homotopy theoretic considerations. 1 From compact Lie groups to p-co...

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Probability on Compact Lie Groups

DEFINABLE GROUPS AND COMPACT p-ADIC LIE GROUPS

We formulate a version of the o-minimal group conjectures from [11], which is appropriate for groups G definable in a (saturated) p-adically closed field K, We discuss the conjectures in two cases, when G is defined over Qp and when G is of the form E(K) for E an elliptic curve over K.

The Transfer and Compact Lie Groups

Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be /-universal classifying spaces, with p{H, G): BH -» BG the natural projection. Then transfer homomorphisms J\H, G): h(BH) -» h(BG) are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset the...