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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeOct 3rd 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexHi everyone! I'm back from a 2-week vacation without Internet access. It'll take me a little while to catch up on everything, but just so you know, I'm here again now....

   Hi everyone! I’m back from a 2-week vacation without Internet access. It’ll take me a little while to catch up on everything, but just so you know, I’m here again now….

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 3rd 2011
   • (edited Oct 3rd 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexGood to hear that you are back! I was in Pittsburgh last week and spoke with some of the HoTT people there. Only through this conversation has it become clear to me that the HoTT derivation of $$ \pi_1 (S^1) = \mathbb{Z} $$ that you had posted to the blog a while back is regarded as a big achievement in the field! I hear that Joyal is currently following a project for next computing $\pi_3(S^2)$. Sounds like this is something that will keep HoTTists busy for a while. :-)

   Good to hear that you are back!

   I was in Pittsburgh last week and spoke with some of the HoTT people there. Only through this conversation has it become clear to me that the HoTT derivation of

   $$\pi_1 (S^1) = \mathbb{Z}$$

   that you had posted to the blog a while back is regarded as a big achievement in the field! I hear that Joyal is currently following a project for next computing $\pi_3(S^2)$. Sounds like this is something that will keep HoTTists busy for a while. :-)

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 3rd 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexWelcome back! I figured that you were just hunkering down to research and avoiding getting distracted by internet stuff, forgetting that I too take internet-free vacations on occasion. :-)

   Welcome back! I figured that you were just hunkering down to research and avoiding getting distracted by internet stuff, forgetting that I too take internet-free vacations on occasion. :-)

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeOct 3rd 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItex> the HoTT derivation of $\pi_1 (S^1) = \mathbb{Z}$ that you had posted to the blog a while back is regarded as a big achievement in the field! That's nice to hear; I haven't actually talked to any of them in person since the HoTT Oberwolfach meeting. (-: I wonder what approach Joyal is taking to $\pi_3(S^2)$. The "obvious" approach to me is to construct the Hopf fibration and prove the homotopy long exact sequence of a fibration, but it's not obvious to me how to identify the total space of the Hopf fibration as being $S^3$ (or, at least, 2-simply-connected). I guess that that approach would also first involve proving $\pi_n(S^n)=\mathbb{Z}$ at least for small $n$, which one could maybe do with the Freudenthal suspension theorem.

   the HoTT derivation of $\pi_1 (S^1) = \mathbb{Z}$ that you had posted to the blog a while back is regarded as a big achievement in the field!

   That’s nice to hear; I haven’t actually talked to any of them in person since the HoTT Oberwolfach meeting. (-: I wonder what approach Joyal is taking to $\pi_3(S^2)$. The “obvious” approach to me is to construct the Hopf fibration and prove the homotopy long exact sequence of a fibration, but it’s not obvious to me how to identify the total space of the Hopf fibration as being $S^3$ (or, at least, 2-simply-connected). I guess that that approach would also first involve proving $\pi_n(S^n)=\mathbb{Z}$ at least for small $n$, which one could maybe do with the Freudenthal suspension theorem.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 3rd 2011
   • (edited Oct 3rd 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, apparently Joyal is going via the Hopf fibration. But that's already all I have heard about it. (Apart from giving a talk to the whole group, I mostly chatted with Krzysztof Kapulkin, who told me these things.)

   Yes, apparently Joyal is going via the Hopf fibration. But that’s already all I have heard about it. (Apart from giving a talk to the whole group, I mostly chatted with Krzysztof Kapulkin, who told me these things.)