Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Kitazawa, Naoki"'
Autor:
Kitazawa, Naoki
We characterize $3$-dimensional manifolds represented as connected sums of Lens spaces, copies of $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions. This adds to our previous result around 2024, classifying Morse fun
Externí odkaz:
http://arxiv.org/abs/2412.11397
Autor:
Kitazawa, Naoki
As a topic of mathematics, "arrangements", systems of hyperplanes, circles, and general (regular) submanifolds, attract us strongly. We present a natural elementary study of arrangements of circles. It is also a kind of new studies. Our study is clos
Externí odkaz:
http://arxiv.org/abs/2412.03846
Autor:
Kitazawa, Naoki
Morse functions are important objects and tools in understanding topologies of manifolds since the 20th century. Their classification has been natural and difficult problems, and surprisingly, this is recently developing. Since the 2010's, results fo
Externí odkaz:
http://arxiv.org/abs/2411.15943
Autor:
Kitazawa, Naoki
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 surjection o
Externí odkaz:
http://arxiv.org/abs/2312.10646
Autor:
Kitazawa, Naoki
The Reeb graph of a smooth function is a graph being a natural quotient space of the manifold of the domain and the space of all connected components of preimages. Such a combinatorial and topological object roughly and compactly represents the manif
Externí odkaz:
http://arxiv.org/abs/2307.07122
Autor:
Kitazawa, Naoki
Previously, we have systematically constructed explicit real algebraic functions which are represented as the compositions of smooth real algebraic maps whose images are domains surrounded by hypersurfaces of degree 1 or 2 with canonical projections.
Externí odkaz:
http://arxiv.org/abs/2304.07540
Autor:
Kitazawa, Naoki
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining non-proper sm
Externí odkaz:
http://arxiv.org/abs/2304.02372
Autor:
Kitazawa, Naoki
As a pioneering work we construct explicit real algebraic functions which may have both compact and non-compact preimages. The author has obtained explicit real algebraic functions with preimages satisfying some nice conditions. More precisely, we ha
Externí odkaz:
http://arxiv.org/abs/2303.14988
Autor:
Kitazawa, Naoki
We present new real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so-called "transversality" as follows. Explicit information on important
Externí odkaz:
http://arxiv.org/abs/2303.10723
Autor:
Kitazawa, Naoki
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 functions o
Externí odkaz:
http://arxiv.org/abs/2303.00953