Subject: more on homology spheres From: Yuli Rudyak Date: Wed, 29 Sep 2004 13:23:36 -0400 (EDT) To: dmd1@lehigh.edu Dear Don, Here is a remark concerning homology spheres. Let $X$ be a homological disc. John Klein noticed that $[X,BO]$ is one-point set, using that $BO$ is a loop space. More simple argument for almost paralleizability of homology spheres (note that they are orientable): The map $[X,BSO]$ is one-point set because of the obstruction theory. We do not have twisted coefficient since $BSO$ is simply connected, while $X$ has trivial homology. Anyway, it is very good that the list produced such pretty claim (stable parallelizability of homology spheres). Yuli Dr. Yuli B. Rudyak Department of Mathematics University of Florida 358 Little Hall PO Box 118105 Gainesville, FL 32611-8105 USA TEL: (+1) 352-392-0281 ext. 319(office) TEL: (+1) 352-381-8497(home) FAX: (+1) 352-392-8357 URL: http://www.math.ufl.edu/~rudyak/