Skip to main content
14 events
when toggle format what by license comment
Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Dec 16, 2013 at 23:28 comment added Ricardo Andrade @Igor Belegradek, it was my pleasure. I do apologize for the confusion.
Dec 16, 2013 at 22:57 comment added Ricardo Andrade @Igor Belegradek, to clarify, I have actually not changed the meaning of $N$ from your question. When I write $N$ in my answer, I mean the same $N$ you do in the question. Your map is called $i$ in my answer, and Tom's map is called $r$. $V$ is an open manifold (diffeomorphic to the interior of $N$) which contains $N$ as in your question. Moreover, $N_0$ is a compact manifold (diffeomorphic to $N$) which is contained in the interior of $N$. Does that make things clearer?
Dec 16, 2013 at 22:46 history edited Ricardo Andrade CC BY-SA 3.0
added 25 characters in body
Dec 16, 2013 at 22:32 comment added Ricardo Andrade @Igor Belegradek: Ah, now I think I understand the problem... I have actually not changed the meaning of $V$ at all. By $V$ I still mean a manifold obtained from $N$ by gluing an open collar onto the boundary. I will add that clarification to the answer.
Dec 16, 2013 at 22:27 comment added Igor Belegradek There is a notation mismatch (which maybe the cause of my confusion). In your notation $V=Int(N)$ and $N_0$ is $N$ minus open collar, while I denote $N_0$ by $N$. If it is not too much trouble, could you keep the notations as in my question, i.e. change $N_0$ to $N$, and change $N$ so something else?
Dec 16, 2013 at 22:25 history edited Ricardo Andrade CC BY-SA 3.0
added 25 characters in body
Dec 16, 2013 at 22:22 comment added Ricardo Andrade @Igor Belegradek, then I believe I correctly understood the definition of your map. So I am confused as to what issue you find with my explanation above. Perhaps it is related to how you have changed notation from your question to the comment above? In my answer, I described your map as taking $\phi\in \operatorname{Diff}(N)$ to $l\circ\phi$, where $l:N\to V$ is the inclusion. Can you please clarify where you think there is a problem with my answer?
Dec 16, 2013 at 22:16 history edited Ricardo Andrade CC BY-SA 3.0
edited body
Dec 16, 2013 at 22:16 comment added Igor Belegradek My map takes a diffeomorphism $\phi\in Diff(N)$ to $k\circ\phi$, where $k: N\to V$ is the inclusion.
Dec 16, 2013 at 22:12 comment added Ricardo Andrade @Igor Belegradek, to make things clearer, if $\iota$ denotes the inclusion, by "post-composing with the inclusion" do you mean $- \circ \iota$?
Dec 16, 2013 at 22:07 history edited Ricardo Andrade CC BY-SA 3.0
added 28 characters in body
Dec 16, 2013 at 22:07 comment added Igor Belegradek The map in Goodwillie's answer is post-composing with the inclusion--mine is pre-composing with the inclusion.
Dec 16, 2013 at 21:58 history answered Ricardo Andrade CC BY-SA 3.0