Reputation
538
Next privilege 1,000 Rep.
Create new tags
Badges
4 10
Newest
 Enlightened
Impact
~3k people reached

  • 0 posts edited
  • 0 helpful flags
  • 45 votes cast
Jun
3
comment Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$
@Crostul: It's about half-way down. Is $R/(x_0^\infty,\ldots,x_{n-1}^\infty) \simeq R/I^\infty$? The rest is an attempt at a proof, but I'm not sure if it is correct!
Jun
3
revised Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$
consistency with $R$ and $A$
Jun
3
asked Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$
May
22
awarded  Enlightened
May
22
awarded  Nice Answer
Feb
27
awarded  Yearling
Dec
13
awarded  Caucus
Oct
18
awarded  Autobiographer
Aug
18
answered homotopy class of maps in terms of homotopy groups of spectra
Aug
18
comment homotopy class of maps in terms of homotopy groups of spectra
This can't work for spaces since $[X,Y]$ is in general only a set. If you work with spectra instead of spaces (the very open) Freyd's generating hypothesis is that for finite spectra $X$ and $Y$ the natural map $[X,Y] \to \text{Hom}_{\pi_* S}(\pi_*X,\pi_* Y)$ is a monomorphism (which Freyd shows actually implies it is an isomorphism).
Jul
22
answered Refining homotopy commutative maps of spectra to maps of E_{\infty}-ring spectra
Mar
11
comment A group-like topological monoid is a loop space
Opps, I have no idea how that happened. I think I meant to link to this: math.stanford.edu/~carym/bar.pdf
Mar
11
comment A group-like topological monoid is a loop space
This probably depends on your model for $BM$, but see, for example, math.stackexchange.com/questions/704397/…
Feb
27
awarded  Yearling
Feb
19
comment A question about the universal coefficient theorem.
I think if you're careful about it, you'll find that the maps can be chosen to be $R$-module maps, but that the splitting is not one of $R$-modules
Jan
31
comment Universal Coefficient Theorem - what kind of morphisms?
But here you know what the map $H_n(X) \otimes \mathbb{Q} \to H_n(X;\mathbb{Q})$ is - and you know (on the chain level) where the module structure is coming from
Jan
30
comment Universal Coefficient Theorem - what kind of morphisms?
The point is that $H_1(X;\mathbb{Q})\simeq H_1(X) \otimes \mathbb{Q}$ both as abelian groups and as a $\mathbb{Q}$-vector space
Jan
30
comment Universal Coefficient Theorem - what kind of morphisms?
As an example, what can you say about $H_1(X;\mathbb{Q})$ as an abelian group, and as a vector space?
Jan
27
comment Cup Product Structure on the n-Torus
See the bottom of pp. 242: math.cornell.edu/~hatcher/AT/ATcapprod.pdf
Nov
19
comment If the connected sum of a manifold $M$ with itself gives back $M$, does it imply $M$ is a sphere?
@JasonDeVito: Oh, I totally misread the question! Hmm, now I'd like to see it as well