Related papers: Lifts of spherical Morse functions
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…
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…
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 generalize the class of so-called special generic maps.…
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…
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…
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…
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…
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…
Morse functions with exactly two singular points on homotopy spheres and canonical projections of spheres are generalized as special generic maps. A special generic map is, roughly, a smooth map represented as the composition of a smooth…
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 smooth maps whose codimensions are not positive such as Morse…
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…
Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important…
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,…
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…
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 are simplest examples of such maps and manifolds admitting…
In geometry, understanding the topologies and the differentiable structures of manifolds in constructive ways is fundamental and important. It is in general difficult, especially for higher dimensional manifolds. The author is interested 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…
Special-generic-like maps or SGL maps are introduced by the author motivated by observing and investigating algebraic topological or differential topological properties of manifolds via nice smooth maps whose codimensions are negative. The…
Round fold maps are smooth maps on closed manifolds which are locally represented as the product maps of Morse functions and identity maps on open disks and whose singularity is realized as concentrically embedded spheres. The author…
In this paper, as a fundamental study on the theory of Morse functions and their higher dimensional versions or fold maps and applications to geometric theory of manifolds, which were started in 1950s by differential topologists such as…