5 papers
Morse functions with regular level sets consisting of -dimensional spheres, -dimensional tori, or Klein Bottles
Naoki Kitazawa
In this paper, we study Morse functions with regular level sets consisting of spheres, tori, or Klein Bottles on -dimensional closed manifolds. We characterize -dimensional m…
Reeb spaces of smooth functions associated to globally similar graphs of smooth functions
Naoki Kitazawa
Previously, we have investigated a natural smooth map onto the region surrounded by the graphs of two smooth real-valued functions in the plane converging to a same value or diverg…
A note on asymptotic behaviors and topological properties of two smooth real-valued functions and several graphs associated to them
Naoki Kitazawa
This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical project…
On reconstructing Morse-Bott functions with prescribed preimages on -dimensional manifolds and conditions for the reconstruction
Naoki Kitazawa
We present conditions for reconstruction of Morse-Bott functions with prescribed preimages on -dimensional manifolds. The present work strengthens a previous result for the Mors…
On reconstructing Morse functions with prescribed level sets on -dimensional manifolds and a necessary and sufficient condition for the reconstruction
Naoki Kitazawa
We discuss a necessary and sufficient condition for reconstruction of Morse functions with prescribed (regular) level sets on -dimensional manifolds. The present work strengthen…