From representation theory to homotopy groups / Donald M. Davis.

Format:

Book

Author/Creator:

Davis, Donald M., 1945- author.

Series:

Memoirs of the American Mathematical Society ; no. 759.

Memoirs of the American Mathematical Society, 0065-9266 ; number 759

Language:

English

Subjects (All):

Homotopy groups.

Representations of groups.

Physical Description:

1 online resource (65 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.

Contents:

Intro

Contents

1. Introduction

2. Representation theory and ψ[sub(2)] in K-theory

3. Nice form for ψ[sub(2)] in PK[sub(l)](E[sub(8)])[sub(5)] and PK[sup(1)](X)

4. Determination of υ[sup( 1)][sub(1)]π[sub(2m)](E[sub(8)]

5)

5. Determination of υ[sup( 1)][sub(1)]π[sub(2m 1)(E[sub(8)]

6. Calculation of υ[sup( 1)][sub(1)]π[sub(*)](E[sub(8)]

3

7. LiE program for computing λ[sup(2)] in R(E[sub(8)])

8. Analysis of F[sub(4)] and E[sub(7)] at the prime 3

References.

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 48-50).

Description based on print version record.

ISBN:

1-4704-0357-9