Timeline for References for variations of Seifert–van Kampen's theorem: HNN extensions and "sensible" intersections

7 events

when toggle format	what		by	license	comment
Jun 26 at 9:11	comment	added	Allen Hatcher		For the second variant, there is some discussion of HNN extensions in Example 1B.13 of my book, but this doesn't quite give what you're looking for. I'll try to include this somewhere in the revised edition.
Jun 26 at 9:01	comment	added	Allen Hatcher		As Andy Putman said, the CW variant is in my book. It's in the paragraph following the proof of Proposition A.5 in the Appendix. The book should have included a cross reference to this in the discussion of van Kampen's theorem in Chapter 1, but I'm revising the book and will add a cross reference.
Jun 25 at 21:41	comment	added	Andy Putman		(your second conclusion is something I often give as an exercise, and if a grad student can’t prove it for themselves they don’t really understand SvK)
Jun 25 at 21:40	comment	added	Andy Putman		For the CW complex variant, what you need is that a subcomplex $Y$ of a CW complex $X$ has an open neighborhood that deformation retracts to it. Hatcher calls such an $(X,Y)$ a “good pair”, and verifies this (if I recall correctly) in the appendix on the topology of CW complexes.
Jun 25 at 21:35	comment	added	Ryan Budney		All these results follow from considering the $2$-skeleton of the associated CW complex and applying SVK. I don't think of them as folklore, but just a step away from the basic theory.
Jun 25 at 21:18	history	edited	LSpice	CC BY-SA 4.0	Typos
Jun 25 at 14:08	history	asked	NWMT	CC BY-SA 4.0