# Open Problems in Algebraic Topology and Homotopy Theory

Some time ago (I see it was initially written before 1999?) Mark Hovey assembled a list of open problems in algebraic topology. The list can be found here. Some of the problems I know about have been worked on quite a bit since the time of writing. The list is very good as is, but there must also be a few good additions since 1999. Can someone point me to a more recent list of open problems in algebraic topology? My googling isn't turning up much else. Thank you!

• Although I have great respect for Mark Hovey, I have always felt this list to be very narrow in scope. For example, there is nothing about calculus of homotopy functors on it. Also, The list is quite silent about the study of the algebraic topology of manifolds. – John Klein Jul 4 '13 at 15:40
• Hopefully he doesn't mind me advertising for him, but Tyler Lawson is presently assembling such a list which should be made public fairly soon. If you're anxious to see it, then you might want to email him about it, in case he doesn't see this question on his own. – Eric Peterson Jul 4 '13 at 17:59
• He's Tyler Lawson. He sees everything – David White Jul 4 '13 at 18:52
• Some of Tyler's remarks (and descriptions of beautiful, beautiful art) can be found here (notes written by Paul VanKoughnett at Talbot): math.mit.edu/conferences/talbot/2013/19-Lawson-thefuture.pdf – Dylan Wilson Jul 5 '13 at 0:23
• Yes, there is currently such an effort (though it is not even remotely just an effort of mine). I would really hesitate to suggest when it might be public. – Tyler Lawson Jul 5 '13 at 6:04

Further comment: The origin of this work was methodological (does that count as a "problem"?). In the 1960s, writing the first edition of the book which is now "Topology and Groupoids" (2006), I convinced myself that all of $1$-dimensional homotopy theory was better expressed in terms of groupoids rather than groups. So the next question was: are groupoids useful, or not, or to what extent, in higher dimensional homotopy theory? Trying to find answers to this has been a lot of fun for all concerned, though the 1981 published work with Philip Higgins was described once to me by Michael Barratt as "Carved out of solid rock, and pursued in the teeth of opposition".