24 citations · 171 across the 71 of their papers we have counts for
14 papers · 1 filter
Round fold maps of n--dimensional manifolds into
Naoki Kitazawa, Osamu Saeki
We determine those smooth --dimensional closed manifolds with which admit round fold maps into , i.e.\ fold maps whose critical value sets consist…
Characterizing families of graph manifolds via suitable classes of simple fold maps into the plane and embeddability of the Reeb spaces in some 3-dimensional manifolds
Naoki Kitazawa
Graph manifolds form important classes of -dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are n…
Round fold maps on --manifolds
Naoki Kitazawa, Osamu Saeki
We show that a closed orientable 3--dimensional manifold admits a round fold map into the plane, i.e. a fold map whose critical value set consists of disjoint simple closed curves…
Surgery operations to fold maps to construct fold maps whose restrictions to the singular sets may not be embeddings
Naoki Kitazawa
Constructing Morse functions and their higher dimensional versions or fold maps is fundamental, important and challenging in investigating the topologies and the differentiable str…
Maps on manifolds onto graphs locally regarded as the quotient maps onto Reeb spaces of some differentiable maps and a new construction problem
Naoki Kitazawa
The Reeb space of a function or a map on a manifold is defined as the space of all connected components of preimages and represents the manifold compactly. In fact, Reeb spaces are…
On Reeb graphs induced from smooth functions on closed or open manifolds
Naoki Kitazawa
For a smooth function on a smooth manifold of a suitable class, the space of all connected components of preimages is the graph and called the {\it Reeb graph}. Reeb graphs are fun…
An elementary study on realizable changes of homology groups of Reeb spaces of fold maps by fundamental surgery operations
Naoki Kitazawa
In the singularity and differential topological theory of Morse functions and higher dimensional versions or fold maps and application to algebraic and differential topology of man…
Explicit remarks on the torsion subgroups of homology groups of Reeb spaces of explicit fold maps
Naoki Kitazawa
Fold maps are higher dimensional versions of Morse functions and fundamental and important tools in studying algebraic and differential topological properties of manifolds: as the…
On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values
Naoki Kitazawa
The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the…
Structures of cobordism-like modules induced from generic maps of codimension -2
Naoki Kitazawa
The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions…
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…