Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Mathematics
Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz
Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz
Dartmouth Scholarship
Let X be an H-space of the homotopy type of a connected, finite CW-complex, f : X→X any map and pk : X→X the kth power map. Duan proved that pkf : X → X has a fixed point if k ≥ 2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map …