most recent 30 from http://mathoverflow.net 2013-05-24T17:01:32Z http://mathoverflow.net/feeds/question/97350 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/97350/how-many-model-category-structures-are-there-on-top JeremyLane 2012-05-18T20:26:29Z 2012-05-18T22:52:39Z

<p>I recently started learning a little model <em>category</em> theory and in particular I found <a href="http://mathoverflow.net/questions/29635/what-determines-a-model-structure/29653#29653" rel="nofollow">this</a> nice exercise. I only know a little topology, but this prompted me to wonder how many model category structures there may be on Top. I am aware of three: Serre fibrations and weak homotopy equivalences, Hurewicz fibrations and homotopy equivalences, and the usual model category of rational homotopy theory <a href="http://folk.uio.no/paularne/SUPh05/DS.pdf" rel="nofollow">[Dwyer and Spalinski]</a>. A secondary question could be how many homotopy theories there are since it is known that the first two I mention give the same homotopy theory.</p> <p>*This question is a little out of my league right now. I hope that is ok. I'm not even sure how difficult this question is.</p>