Problem 11.5 — Generalize the infinitesimal presentation of the Torelli Lie algebra given by Hain [29] to the case of the group of h…
v1.3 research notesGeneralize the infinitesimal presentation of the Torelli Lie algebra given by Hain [29] to the case of the group of homology cobordism classes of homo...
Problem 12.1 — Prove that the above characteristic classes induce surjective homomorphism H3(BDiffδ +Σg; Z)−→R2 for any g.
v1.3 research notesProve that the above characteristic classes induce surjective homomorphism H3(BDiffδ +Σg; Z)−→R2 for any g. The cohomology classes in (22) are stable w...
Problem 12.2 — Study whether the homology groups of BDiffδ +Σg stabilize with respect to g or not.
v1.3 research notesStudy whether the homology groups of BDiffδ +Σg stabilize with respect to g or not. The same problem for the group SympδΣg. 374 S. Morita Acknowledgmen...
Question — Which properties of the braid groups can be extended to the mapping class groups?
v1.3 research notesWhich properties of the braid groups can be extended to the mapping class groups?...
Major problems 1 — The biggest problem, in my opinion, is to come up with a specific vision of where homotopy theory shou…
v1.3 research notesThe biggest problem, in my opinion, is to come up with a specific vision of where homotopy theory should go, analogous to the Weil conjectures in alge...
Applications 2 — Neil Strickland points out that several different moduli spaces are used in differential geometry and…
v1.3 research notesNeil Strickland points out that several different moduli spaces are used in differential geometry and physics. For example, there is the moduli space ...
Axiomatic stable homotopy 10 — What is the endomorphism ring of the identity functor on the stable homotopy category?
v1.3 research notesWhat is the endomorphism ring of the identity functor on the stable homotopy category? The ring Z splits off this ring, including by multiples of the ...
Model categories 10 — Is every monoidal model category Quillen equivalent to a simplicial monoidal model category?
v1.3 research notesIs every monoidal model category Quillen equivalent to a simplicial monoidal model category? This would remove the loose end in my book on model categ...
Model categories 13 — Find a model category you can prove is not cofibrantly generated.
v1.3 research notesFind a model category you can prove is not cofibrantly generated. This is just an annoyance, not a very significant problem, but it has been bugging m...