Timeline for Codimension Two Embeddings in Goodwillie-Weiss Manifold Calculus, and the Difficulty of Fundamental Groups

Current License: CC BY-SA 3.0

8 events

when toggle format	what		by	license	comment
Jun 20, 2012 at 16:08	history	edited	Hiro Lee Tanaka	CC BY-SA 3.0	improved formatting, inserting `operatorname.'
May 20, 2012 at 16:34	history	edited	Hiro Lee Tanaka	CC BY-SA 3.0	edited title
May 20, 2012 at 5:09	comment	added	Tom Goodwillie		Yes, and 2 and 3 use the fact that the fundamental group is unchanged by cutting out something of codim $\ge 3$, though 1 does not.
May 20, 2012 at 2:43	comment	added	John Klein		I just wish to remark that the current proof of the multiple disjunction statements for smooth embeddings involve several steps: 1. reduction to statements about block embeddings (using Tom's thesis). 2. reduction of the latter to statements about Poincare embeddings (using surgery theory). 3. Proof of the statements about Poincare embeddings from (using homotopy theory). Each of these steps requires the codimension $\ge 3$ hypothesis somewhere along the way.
May 20, 2012 at 0:15	comment	added	Hiro Lee Tanaka		That's really amusing -- I didn't realize! The first sentence of the question also could be a question about usual calculus (on manifolds). I've changed the title to be more explicit. Thanks, Tom.
May 20, 2012 at 0:10	history	edited	Hiro Lee Tanaka	CC BY-SA 3.0	Changed title following Tom's comment
May 19, 2012 at 17:16	comment	added	Tom Goodwillie		The typical reader of this question will assume that "manifold calculus" is something like "calculus on manifolds", whereas actually you are referring to one of the several versions of this pet idea of mine called the "calculus of functors". But the really funny thing is that even I somehow failed to realize what the question was about from just looking at the title! I will try to come up with a sensible answer, but not this minute.
May 19, 2012 at 6:53	history	asked	Hiro Lee Tanaka	CC BY-SA 3.0