Title: Fusion systems and group actions with abelian isotropy subgroups
 
Authors: {\" O}zg{\" u}n {\" U}nl{\" u} and Erg{\" u}n Yal{\c c}{\i}

Status: To appear in Proceedings of the Edinburgh Mathematical Society.

Address: 
Department of Mathematics, Bilkent University,
06800 Bilkent, Ankara, Turkey

Email1: unluo@fen.bilkent.edu.tr
Email2: yalcine@fen.bilkent.edu.tr 


Abstract: We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times \dots \times \bbS^{n_k}$ for some positive integers $n_1,\dots, n_k$. We construct these actions using a recursive method, introduced in an earlier paper, that involves abstract fusion systems on finite groups. As another application of this method, we prove that every finite solvable group acts freely and smoothly on some product of spheres with trivial action on homology.