Related papers: Smooth maps like special generic maps
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…
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…
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…
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…
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…
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…
As Reeb's theorem shows, Morse functions with exactly two singular points on closed manifolds are very simple and important. They characterize spheres whose dimensions are not $4$ topologically and the $4$-dimensional unit sphere. Special…
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…
We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exactly two singular points on closed manifolds, characterizing…
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…
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…
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dimensional standard spheres. The class of such maps also…
Morse functions with exactly two singular points on spheres and canonical projections of spheres belong to the class of a certain good class of smooth maps: special generic maps. We mainly investigate information on cohomology of closed and…
The class of special generic maps is a natural class of smooth maps containing Morse functions on spheres with exactly two singular points and canonical projections of unit spheres. We find new restrictions on such maps on $6$-dimensional…
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…
We prove the non-existence of special generic maps on complex projective space as our extended new result. Simplest special generic maps are Morse functions with exactly two singular points on spheres, or Morse functions in Reeb's theorem,…
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 higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except $4$-dimensional cases: in these cases standard spheres are characterized. Canonical…
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…
The present paper finds new necessary and sufficient conditions for $6$-dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into certain Euclidean spaces. The class of special generic maps…