15,982 reputation
14677
bio website math.uchicago.edu/~may
location US
age 74
visits member for 3 years, 9 months
seen 4 hours ago
At the University of Chicago since 1967. Mainly known as an algebraic topologist.

6h
comment The topology of the classifying space of U(n)
Standard: rational homotopy equivalence, meaning the two spaces become homotopy equivalent after rationalizing (when the Z's become Q's on the right). A suitable map from left to right is given by the Chern classes.
1d
answered Is there an analog of the Barratt-Eccles construction for E_∞-groups and E_∞-rings?
Aug
24
comment PBW proof proposal
This is a sketch of a standard proof, and one does not have to restrict to characteristic zero. See Section 22.2 of ``More Concise Algebraic Topology" by Kate Ponto and myself for a recent version, which deals with graded Lie algebras.
Aug
7
awarded  model-categories
Aug
7
answered Is the category of $G$-spaces a model category?
Jul
31
awarded  Nice Answer
Jul
31
answered How much of homotopy theory can be done using only finite topological spaces?
Jul
29
comment Fibrations and Cofibrations of spectra are “the same”
Just a small quibble. Fibration sequences and cofibration sequences give two structures of triangulated category to the homotopy category of spectra. One is the negative of the other: (f,g,h) is an exact triangle in one if and only if (-f,-g,-h) is an exact triangle in the other. So they are not quite ``the same''.
Jul
28
comment Adams' theorems on the Hopf-Whitehead J-homomorphism
Right, Dustin: the space F = GL_1(S) is both additive (F) and multiplicative (GL_1(S)), and it is split by an exponential equivalence from J with its additive structure to J with its multiplicative structure.
Jul
28
comment RO(G) grading of Mackey functors
I think you are still missing the point: many inequivalent representations have homotopy equivalent S^V: that is, as I said in the first place, the map from RO(G) to Pic is neither injective or surjective. This is not something you expect to calculate naively.
Jul
28
comment RO(G) grading of Mackey functors
What it is is implicit in my answer: smashing with S^V gives you an action of the abelian group RO(G) on HoGS that factors through Pic(HoGS). You do not see the multiplication of RO(G) that way, so it is in no sensible sense an action of RO(G).
Jul
28
comment RO(G) grading of Mackey functors
Not an operation of RO(G). You've got to learn the math.
Jul
27
answered Algebraic $K$-theory of algebras in symmetric spectra: reference
Jul
27
comment RO(G) grading of Mackey functors
Delete the first use of ``how''. No meaning, no formula.
Jul
26
answered RO(G) grading of Mackey functors
Jul
12
comment Why localize spaces with respect to homology?
``What we really care about?" Mike, that depends on whether or not one is interested in applications and calculations.
Jul
10
comment Why localize spaces with respect to homology?
Also, I would like to emphasize Craig's point. It is not that things are simpler but that there are new phenomena invisible before localization. Adams already was well aware of this. He implicitly proved that localizations of spheres at odd primes are H-spaces in a 1960 paper, and by the time of the notes he of course understood the role of localization in that statement.
Jul
10
comment Why localize spaces with respect to homology?
Not from the text of the notes, but Frank was then visiting me at Chicago, and I can attest that not so far back in his mind was thinking about periodic localizations and periodicity phenomena in the stable homotopy groups of spheres, which he had been thinking about since 1960 or so.
Jul
8
awarded  Nice Answer
Jul
8
comment Why localize spaces with respect to homology?
Thanks Vidit. Teach me privately how to do that, please.