24 citations · 171 across the 71 of their papers we have counts for
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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…
Real algebraic functions on closed manifolds whose Reeb spaces are given graphs
Naoki Kitazawa
In our paper, we construct a real-algebraic function whose Reeb (Kronrod-Reeb) graph is a graph respecting some algebraic domain: a graph for this is called Poincaré-Reeb graph. Th…
Smooth maps like special generic maps
Naoki Kitazawa
In our paper, we introduce special-generic-like maps or SGL maps as smooth maps and study their several algebraic topological and differential topological properties. The new class…
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 Reeb graphs induced from smooth functions on 3-dimensional closed manifolds which may not be orientable
Naoki Kitazawa
The Reeb space of a smooth function is a topological and combinatoric object and fundamental and important in understanding topological and geometric properties of the manifold of…
Smooth functions with simple structures on 3-dimensional closed manifolds with prescribed Reeb graphs and preimages
Naoki Kitazawa
We give a new answer to so-called realization problems of graphs as Reeb graphs of smooth functions with prescribed preimages of regular values having nice structures. We present a…
Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages
Naoki Kitazawa
The present paper is on a new result on so-called realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages. The Reeb graph of a smooth function is…
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…
Global topologies of Reeb spaces of stable fold maps with non-trivial top homology groups
Naoki Kitazawa
The Reeb space of a continuous map is the space of all (elements representing) connected components of preimages endowed with the quotient topology induced from the natural equival…
Simple polyhedra homeomorphic to Reeb spaces of stable fold maps
Naoki Kitazawa
Simple polyhedra are -dimensional polyhedra and important objects in low-dimensional geometry and in the applications of {\it fold} maps, defined as smooth maps regarded as high…
Branched surfaces homeomorphic to Reeb spaces of simple fold maps
Naoki Kitazawa
Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of…
Products of elements of cobordism-like modules induced from generic maps
Naoki Kitazawa
Recently the author has introduced cobordism-like modules induced from generic maps whose codimensions are negative. They are generalizations of cobordism modules of manifolds. The…
Explicit round fold maps on some fundamental manifolds
Naoki Kitazawa
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth m…
Constructions of round fold maps on circle bundles
Naoki Kitazawa
{\it Fold maps} are fundamental tools in generalizing the theory of Morse functions and its application to studies of geometric properties of manifolds. One of the fundamental and…
Constructions of round fold maps on bundles
Naoki Kitazawa
In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more gen…