Related papers: Explicit round fold maps on some fundamental manif…
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…
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…
{\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…
In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes…
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…
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…
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…
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…
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…
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…
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…
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 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…
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…
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…
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…
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.…
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…
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…