Related papers: Round fold maps into the plane on some $7$-dimensi…

Fold maps are smooth maps at each singular point of which it is represented as the product map of a Morse function and the identity map. Round fold maps are, in short, such maps the sets of all singular points of which are embedded…

We have been interested in understanding the class of 7-dimensional closed and simply-connected manifolds in geometric and constructive ways. We have constructed explicit fold maps, which are higher dimensional versions of Morse functions,…

This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…

Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…

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 manifolds. Round fold maps were introduced as stable fold…

7-dimensional closed and simply-connected manifolds have been attractive as central and explicit objects in algebraic topology and differential topology of higher dimensional closed and simply-connected manifolds, which were studied…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…

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. Classes of special generic maps and round fold maps are…

{\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 important problems in the theory of fold maps is to…

Stable fold maps are fundamental tools in studying a generalized theory of the theory of Morse functions on smooth manifolds and its application to geometry of the manifolds. It is important to construct explicit fold maps systematically to…

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…

Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In…

Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…

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 fold map such that the Morse function can be taken as a…

Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on…

The canonical projections of the unit spheres are generalized to special generic maps and round fold maps, for example. They are generalizations from the viewpoint of singularity theory of differentiable maps and these maps restrict the…

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 and differential topology of manifolds is fundamental,…

The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

Constructing Morse functions and their higher dimensional versions or fold maps is fundamental, important and challenging in investigating the topologies and the differentiable structures of differentiable manifolds via Morse functions,…