TITLE:
Homotopy representations of Spin(7) and SO(7) at prime 2

AUTHOR:
Krzysztof Ziemianski

AMS CLASSIFICATION:
55R35, 55P35

ADDRESS:
Faculty of Mathematics, Informatics and Mechanics
Warsaw University
Banacha 2
02-097 Warszawa
POLAND

E-MAIL:
ziemians@mimuw.edu.pl

ABSTRACT:
A homotopy (complex) representation of a compact connected Lie group L at prime p is a map from BL into the p-completion of the classifying space of the unitary group. In this paper we give a partial classification of homotopy representations of SO(7) and Spin(7) at prime 2. Motiviation for considering this problem is twofold: first, one may hope that it would help to understand maps between classifying spaces. Secondly, construction of a homotopy representation of Spin(7) is a crucial step in the construction of a faithful representation of the 2-compact group DI(4).