Qiaochu Yuan
Reputation
969/1000 score
 17h comment Are there any nontrivial second Hurewicz homomorphisms for familiar compact 6-dimensional manifolds? All of the spaces you describe are just spaces for which $\pi_2$ vanishes, which doesn't have anything to do with the Hurewicz homomorphism. 23h comment Turn off the ovens! An optimization problem This can be solved e.g. using Lagrange multipliers, although there are more elementary methods too. 23h comment Relations between Lie algebras and Lie coalgebras. If it deserves the name, the co-Jacobi identity should just be the dual of the Jacobi identity. 1d comment When does normal maximal subgroup have prime index? Do you mean "normal maximal" or "maximal normal"? 1d comment Is every linear representation of a group $G$ on $k[x_1,\dots,x_n]$ a dual representation? @darij: asking for an algebra automorphism is not enough; for example, $G$ could be a cyclic group acting by rotation around a point other than the origin. You need a graded algebra automorphism, but at that point the statement is almost tautological. 1d answered Representation of a group and its quotient 1d comment Covering map in the context of Riemann Surfaces and Algebraic Topology In the study of Riemann surfaces it's typical to study branched covers, not covers. Branched covers fail to be local homeomorphisms at a finite set of points. It's unclear to me if this is what your professor is talking about, or if they're talking about the fact that in general being a local homeomorphism isn't enough to be a covering map. 1d comment Does $C^*(G) \cong C^*(H)$ imply that $\mathbb{C}G \cong \mathbb{C}H$? @Mike: the group algebras aren't quite the noncommutative polynomial rings; you need to invert the generators. But yes, these are never isomorphic, and can be distinguished e.g. by the Krull dimension of their abelianizations. 1d comment Does $C^*(G) \cong C^*(H)$ imply that $\mathbb{C}G \cong \mathbb{C}H$? If the groups aren't discrete then what do you mean by their group algebras? 1d answered Does $C^*(G) \cong C^*(H)$ imply that $\mathbb{C}G \cong \mathbb{C}H$? 1d comment Day convolution intuition Work through the special case where the monoidal category is discrete. 2d answered How does one compute the Hurewicz homomorphism for a (symplectic) nilmanifold? 2d revised The configuration space of directed great circles on the sphere added 88 characters in body 2d answered Proving trefoil group is isomorphic to a fundamental group. 2d answered The configuration space of directed great circles on the sphere 2d answered Is the global sections functor on smooth manifolds an embedding? 2d comment Is the global sections functor on smooth manifolds an embedding? What is an embedding of categories? You mean a fully faithful functor? 2d answered Generators for a free submodule of a free module 2d awarded Popular Question 2d comment The scope of quantifiers @bof: that seems like a bad convention. Then you constantly need to check whether the sets you're quantifying over are in fact nonempty or not.