4 citations · 9 across the 16 of their papers we have counts for
8 papers · 1 filter
Fundamental examples of Reeb spaces of smooth functions defined from two graphs of smooth functions with same asymptotic behaviors
Naoki Kitazawa
Reeb spaces of (continuous) real-valued functions on (nice) topological spaces are the spaces whose underlying sets consist of all connected components (contours) of their level se…
Smooth functions which are Morse on preimages of values not being local extrema and constructing natural functions of the class on connected sums of manifolds admitting these functions
Naoki Kitazawa
We discuss smooth functions which are Morse on preimages of values not being local extrema. We call such a function internally Morse or I-Morse. The Reeb graph of a smooth function…
Decompositions of manifolds into submanifolds compatible with specific fold maps
Naoki Kitazawa
We present new explicit decompositions of manifolds via so-called fold maps into lower dimensional spaces. Fold maps form a nice class of so-called generic maps, generalizing Morse…
Manifolds admitting special generic maps and their nice generalized multisections
Naoki Kitazawa
We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exact…
On simple classes of special generic maps and round fold maps and fold maps obtained by composing projections
Naoki Kitazawa
Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Cla…
A differential topological study of compact manifolds having simple structures
Naoki Kitazawa
The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are gene…