Timeline for Is transverse intersection continuous?

9 events

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Nov 28 at 0:33	comment	added	Sarah Brooks		Thank you for your insight, Ryan. I was experimenting with constructing a smooth homotopy but the Morse lemma seems to save me work. I guess the first question can probably be answered using a 1-parameter family and an appropriate transversality theorem. I will try to write a solution along these lines.
Nov 27 at 23:43	comment	added	Ryan Budney		Yes, it's continuous. I suppose the way I'd formalize the argument is to put the perturbation (of an individual map or family) into a 1-parameter family, and form the "track" of that family. Then you observe the height function (mapping onto the track parameter) is a Morse function with no critical points. Then you could apply the Morse lemma to get your map between the two intersections. And later observe that map is "small" for small perturbations. That might not be an ideal argument but it's the first that comes to mind.
Nov 27 at 22:29	history	edited	Sarah Brooks	CC BY-SA 4.0	added 19 characters in body
Nov 27 at 21:17	history	edited	Sarah Brooks	CC BY-SA 4.0	edited title
Nov 27 at 21:07	history	edited	Sarah Brooks	CC BY-SA 4.0	added 235 characters in body
Nov 27 at 11:51	history	edited	Sarah Brooks	CC BY-SA 4.0	deleted 224 characters in body
Nov 27 at 11:50	history	edited	Sarah Brooks	CC BY-SA 4.0	added 14 characters in body
S Nov 27 at 11:47	review	First questions
Nov 27 at 12:50
S Nov 27 at 11:47	history	asked	Sarah Brooks	CC BY-SA 4.0