4 citations · 10 across the 33 of their papers we have counts for
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Notes on fold maps obtained by surgery operations and algebraic information of their Reeb spaces
Naoki Kitazawa
The theory of Morse functions and their higher dimensional versions or fold maps on manifolds and its application to geometric theory of manifolds is one of important branches of g…
A new explicit way of obtaining special generic maps into the 3-dimensional Euclidean space
Naoki Kitazawa
A special generic map is a smooth map regarded as a natural generalization of Morse functions with just 2 singular points on homotopy spheres. Canonical projections of unit spheres…
Generalizations of Reeb spaces of special generic maps and applications to a problem of lifts of smooth maps
Naoki Kitazawa
A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smoot…
Lifts of spherical Morse functions
Naoki Kitazawa
In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps an…
Investigating additional structures on preimages of regular values of smooth maps induced from the manifolds via the Reeb spaces and applications
Naoki Kitazawa
The Reeb space of a generic map is the space of all connected components of preimages of the map. Reeb spaces are fundamental and useful tools in the theory of Morse functions and…
Smooth maps compatible with simplicial structures and inverse images
Naoki Kitazawa
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these st…