24 citations · 171 across the 71 of their papers we have counts for
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Restrictions on manifolds admitting certain explicit special-generic-like maps and construction of maps with the manifolds
Naoki Kitazawa
Special-generic-like maps or SGL maps are introduced by the author motivated by observing and investigating algebraic topological or differential topological properties of manifold…
Round fold maps on -dimensional manifolds and their integral and rational cohomology rings
Naoki Kitazawa
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 th…
A class of naturally generalized special generic maps
Naoki Kitazawa
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 th…
New families of manifolds with similar cohomology rings admitting special generic maps
Naoki Kitazawa
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 …
Round fold maps into the plane on some -dimensional closed and simply-connected manifolds
Naoki Kitazawa
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 re…
Special generic maps into on closed and simply-connected manifolds and information on the cohomology of the manifolds
Naoki Kitazawa
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. W…
On the non-existence of special generic maps on complex projective spaces
Naoki Kitazawa
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 singul…
Characterizing certain classes of -dimensional closed and simply-connected manifolds via special generic maps
Naoki Kitazawa
The present paper finds new necessary and sufficient conditions for -dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into cert…
Proofs of the non-existence of special generic maps on the -dimensional complex projective space
Naoki Kitazawa
We prove the non-existence of special generic maps on -dimensional complex projective space as our new result and a corollary by several methods. Special generic maps are genera…
Restrictions on special generic maps into on -dimensional or higher dimensional closed and simply-connected manifolds
Naoki Kitazawa
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…
7-dimensional closed simply-connected and spin manifolds having 2nd integral cohomology classes whose squares are not divisible by 2 and stable fold maps on them
Naoki Kitazawa
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 divisibl…
The topologies and the differentiable structures of the images of special generic maps having simple structures
Naoki Kitazawa
Special generic maps are smooth maps at each singular point of which we can represent as for suitable coordi…
The images of special generic maps of an elementary class
Naoki Kitazawa
The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not -dimensional and the -dimensio…
Notes on explicit special generic maps into Eulidean spaces whose dimensions are greater than 4
Naoki Kitazawa
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dime…
New explicit construction of fold maps on general 7-dimensional closed and simply-connected spin manifolds
Naoki Kitazawa
7-dimensional closed and simply-connected manifolds have been attractive as central and explicit objects in algebraic topology and differential topology of higher dimensional close…
Closed manifolds admitting no special generic maps whose codimensions are negative and their cohomology rings
Naoki Kitazawa
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except -dimensional cases: in thes…
7-dimensional simply-connected spin manifolds whose integral cohomology rings are isomorphic to that of admit round fold maps
Naoki Kitazawa
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…
Special generic maps and fold maps and information on triple Massey products of higher dimensional differentiable manifolds
Naoki Kitazawa
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 c…
Realizing a homology class of a compact manifold by a homology class of an explicit closed submanifold--a new approach to Thom's works on homology classes of submanifolds-
Naoki Kitazawa
It is a classical important problem of differential topology by Thom; for a homology class of a compact manifold, can we realize this by a closed submanifold with no boundary? This…
Explicit fold maps on 7-dimensional closed and simply-connected spin manifolds of new classes
Naoki Kitazawa
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 theor…
Notes on explicit smooth maps on 7-dimensional manifolds into the 4-dimensional Euclidean space
Naoki Kitazawa
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…
On defining products of cobordism classes of Morse functions
Naoki Kitazawa
(Co)bordisms of manifolds and maps are fundamental and important objects in algebraic and differential topology of manifolds and related studies were started by Thom etc.. Cobordis…
Investigating additional structures on preimages of regular values of smooth maps induced from the manifolds via the Reeb spaces and applications
Naoki Kitazawa
The Reeb space of a generic map is the space of all connected components of preimages of the map. Reeb spaces are fundamental and useful tools in the theory of Morse functions and…
Smooth maps compatible with simplicial structures and inverse images
Naoki Kitazawa
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 st…