24 citations · 171 across the 71 of their papers we have counts for
6 papers · 2 filters
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…