Related papers: Surgery operations to fold maps to construct fold …
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…
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 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…
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…
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…
We present new explicit decompositions of manifolds via so-called fold maps into lower dimensional spaces. Fold maps form a nice class of so-called generic maps, generalizing Morse functions naturally. To understand the topologies and the…
There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topological category. From this point of view, Reeb functions on…
Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions 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…
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,…
We study cobordisms of a class of topological operads called ``manifold operads''. These operads are generalizations of the Fulton-MacPherson operad: an operad built from configurations of points in Euclidean space. Cobordism of manifold…
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…
We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole…
Reeb spaces of smooth functions are fundamental and strong tools in understanding manifolds via smooth functions with mild critical points. They are defined as the natural spaces of all connected components of level sets. They are also…
In our paper, we construct a real-algebraic function whose Reeb (Kronrod-Reeb) graph is a graph respecting some algebraic domain: a graph for this is called Poincar\'e-Reeb graph. The Reeb graph of a smooth function is defined as a natural…
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…
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…
On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical…
Nash and Tognoli show that smooth closed manifolds can be the zero sets of some real polynomial maps and non-singular. The canonical projections of spheres naturally embedded in the $1$-dimensional higher Euclidean spaces and some natural…