4 citations · 10 across the 33 of their papers we have counts for
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Notes on explicit smooth maps on 7-dimensional manifolds into the 4-dimensional Euclidean space
Naoki Kitazawa
A fold map is a smooth map at each singular point of which it is represented as the product map of a Morse function and the identity map on an open ball. A special generic map is a…
New observations on cohomology rings of Reeb spaces of explicit fold maps and manifolds admitting these maps
Naoki Kitazawa
As a branch of algebraic and differential topology of manifolds, the theory of Morse functions and their higher dimensional versions or fold maps and its application to algebraic a…
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…