Subject: question for the group From: ogle@math.ohio-state.edu Date: Sat, 29 Jan 2005 09:37:40 -0500 (EST) To: dmd1@lehigh.edu Call a cellular n-complex K resolvable if there is a collapsible n-complex X and a surjective cellular map r:X -> K with contractible point inverses (collapsible means there is a sequence of elementary collapses taking X to *). Obviously, K resolvable => K contractible. Q1. Are there any examples of finite contractible 2-complexes which are not resolvable? Q2. (weaker form) Are there any examples of contractible 2-complexes which are not resolvable? Note: the dunce cap, which is not collapsible, is resolvable.