Merging boundary critical points of a Morse function

Abstract

In 2015, Borodzik, Némethi and Ranicki proved that an interior critical point can be pushed to the boundary, where it splits into two boundary critical points. In this paper, we show that two critical points at the boundary can be, under specific assumptions, merged into a single critical point in the interior. That is, we reverse the original construction.

14 pages, 4 figures; minor revision, version accepted by Proc. AMS