MAXIMAL HOMOTOPY LIE SUBGROUPS OF MAXIMAL RANK

JOHN ANTHONY FROHLIGER, Purdue University

Abstract

Let G be a compact connected Lie group with H a maximal connected compact subgroup of maximal rank. Then there is a fibration (phi):BH (--->) BG with G/H as the fiber space. Suppose there is a space BK whose loop space is homotopy equivalent to a finite complex. Suppose further that there is the composite of fibrations (phi)(,1):BH (--->) BK and (phi)(,2):BK (--->) BG each with fiber homotopy equivalent to a finite complex. The first part of this thesis demonstrates that if BK is not homotopy equivalent to either BH or BG then the Weyl group of H is not a maximal reflection subgroup of the Weyl group of G. The thesis then gives examples where BK is homotopy equivalent to BH or BG even though the Weyl group of H is not a maximal subgroup of the Weyl group of G.

Degree

Ph.D.

Subject Area

Mathematics

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