Connected finite loop spaces with maximal tori

Connected Finite Loop Spaces with Maximal Tori

Finite loop spaces are a generalization of compact Lie groups. However, they do not enjoy all of the nice properties of compact Lie groups. For example, having a maximal torus is a quite distinguished property. Actually, an old conjecture, due to Wilkerson, says that every connected finite loop space with a maximal torus is equivalent to a compact connected Lie group. We give some more evidence...

Finite Loop Space with Maximal Tori have Finite Weyl Groups

Finite Maximal Tori

We examine the structure of compact Lie groups using a finite maximal abelian subgroup A in place of a maximal torus. Just as the classical notion of roots exhibits many interesting subgroups, so the notion of roots of A exhibits many (rather different) interesting subgroups.

Maximal Hamiltonian tori for polygon spaces

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

Rationally Connected Varieties and Loop Spaces

We consider rationally connected complex projective manifolds M and show that their loop spaces—infinite dimensional complex manifolds—have properties similar to those of M . Furthermore, we give a finite dimensional application concerning holomorphic vector bundles over rationally connected complex projective manifolds. 0 Introduction LetM be a complex manifold and r = 0, 1, . . . ,∞. The spac...