论文信息 - FUNCTORIAL DECOMPOSITIONS OF LOOP SPACES OF SUSPENSIONS , AND THEIR RELATION TO REPRESENTATION THEORY

FUNCTORIAL DECOMPOSITIONS OF LOOP SPACES OF SUSPENSIONS , AND THEIR RELATION TO REPRESENTATION THEORY

You might want to give a leisurely exposition of why this is correct as the idea is central to your stuff, and other interesting mathematics. Namely, point out that there is a principal fibration obtained by looping, and there is a section obtained by considering π1. There is a splitting for any principal bundle with section. Thus ΩCP n is homotopy equivalent to the product S × ΩS. This idea is useful in several places. One beautiful application is P. Selick’s product decomposition for the homotopy theoretic fibre of the p-th power map on ΩS. Fred:

F. Cohen | P. Selick | Wu Jie

[1] Jie Wu. A product decomposition of Ω30ΣRP2 , 1998 .

[2] Douglas C. Ravenel,et al. Nilpotence and Periodicity in Stable Homotopy Theory. , 1992 .

[3] Wu Jie,et al. ON FIBREWISE SIMPLICIAL MONOIDS AND MILNOR-CARLSSON’S CONSTRUCTIONS , 1997 .

[4] F. Cohen. On combinatorial group theory in homotopy , 1995 .

[5] Wu Jie. ON COMBINATORIAL CALCULATIONS FOR THE JAMES – HOPF MAPS , 1995 .

[6] Wu Jie. A Product Decomposition of 3 0 Rp 2 , 1995 .