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194 results on '"Kamiyama, Yasuhiko"'

4. On the middle dimensional homology classes of equilateral polygon spaces

Author

Kamiyama, Yasuhiko

Subjects
Mathematics - Algebraic Topology, Mathematics - Algebraic Geometry, Primary 58D29, Secondary 55R80
Abstract

Let $M_n$ be the configuration space of equilateral polygonal linkages with $n$ vertices in the Euclidean plane ${\mathbb R}^2$. We consider the case that $n$ is odd and set $n=2m+1$. In spite of the long history of research, the homology classes in $H_{m-1}(M_n;{\mathbb Z})$ are mysterious and not well-understood. Let $\tau\colon M_n \to M_n$ be the involution induced by complex conjugation. In this paper, we determine the representation matrix of the homomorphism $\tau_\ast\colon H_{m-1}(M_n;{\mathbb Z}) \to H_{m-1}(M_n;{\mathbb Z})$ with respect to a basis of $H_{m-1}(M_n;{\mathbb Z})$.

Published
2015

5. The homology of spaces of polynomials with roots of bounded multiplicity

Author

Kamiyama, Yasuhiko

Subjects
Mathematics - Algebraic Topology, 55P35, 55R20, 58D15
Abstract

Let P_{k, n}^l be the space consisting of monic complex polynomials f(z) of degree k and such that the number of n-fold roots of f(z) is at most l. In this paper, we determine the integral homology groups of P_{k, n}^l., Comment: This is the version published by Geometry & Topology Monographs on 25 February 2008

Published
2009
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6. Configurations and parallelograms associated to centers of mass

Author

Cohen, F R and Kamiyama, Yasuhiko

Subjects
Mathematics - Algebraic Topology, 20F36, 55N25
Abstract

The purpose of this article is to 1. define M(t,k) the t-fold center of mass arrangement for k points in the plane, 2. give elementary properties of M(t,k) and 3. give consequences concerning the space M(2,k) of k distinct points in the plane, no four of which are the vertices of a parallelogram. The main result proven in this article is that the classical unordered configuration of k points in the plane is not a retract up to homotopy of the space of k unordered distinct points in the plane, no four of which are the vertices of a parallelogram. The proof below is homotopy theoretic without an explicit computation of the homology of these spaces. In addition, a second, speculative part of this article arises from the failure of these methods in the case of odd primes p. This failure gives rise to a candidate for the localization at odd primes p of the double loop space of an odd sphere obtained from the p-fold center of mass arrangement. Potential consequences are listed., Comment: This is the version published by Geometry & Topology Monographs on 14 November 2007

Published
2009
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7. Spaces of real polynomials with common roots

Author

Kamiyama, Yasuhiko

Subjects
Mathematics - Algebraic Topology, 55P15, 55P35, 58D15
Abstract

Let RX_{k,n}^l be the space consisting of all (n+1)-tuples (p_0(z),...,p_n(z)) of monic polynomials over R of degree k and such that there are at most l roots common to all p_i(z). In this paper, we prove a stable splitting of RX_{k,n}^l., Comment: This is the version published by Geometry & Topology Monographs on 29 January 2007

Published
2009
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9. The Chow ring of the moduli space and its related homogeneous space of bundles on P^2 with charge 1

Author

Kamiyama, Yasuhiko and Tezuka, Michishige

Subjects
Mathematics - Algebraic Topology
Abstract

For an algebraically closed field K with ch K \not = 2, we determine the Chow ring of the moduli space of holomorphic bundles on a projective plane with the structure group SO(n,K) and half the first Pontryagin index being equal to 1, each of which is trivial on a fixed line and has a fixed holomorphic trivialization there.

Published
2007

13. The Topology of the Configuration Space of a Mathematical Model for Cycloalkenes

Author

Kamiyama, Yasuhiko

Subjects
Mathematics
Abstract

As a mathematical model for cycloalkenes, we consider equilateral polygons whose interior angles are the same except for those of the both ends of the specified edge. We study the configuration space of such polygons. It is known that for some case, the space is homeomorphic to a sphere. The purpose of this chapter is threefold: First, using the h-cobordism theorem, we prove that the above homeomorphism is in fact a diffeomorphism. Second, we study the best possible condition for the space to be a sphere. At present, only a sphere appears as a topological type of the space. Then our third purpose is to show the case when a closed surface of positive genus appears as a topological type.

Published
2022

26. Abstracts of selected papers presented at the 78th general meeting of the Japanese Society of Gastroenterology

Author

Kusano, Motoyasu, Sekiguchi, Toshikazu, Hanyu, Nobuyoshi, Aoki, Teruaki, Matsushima, Yasuhiro, Okamoto, Eizo, Takeda, Yasuo, Takeda, Ryoyu, Miyachi, Masahiko, Nimura, Yuji, Arai, Taidoh, Masuda, Jun, Tanaka, Masao, Ogawa, Yoshiaki, Ura, Kazuhide, Matsumoto, Teiji, Taniyama, K., Kurosawa, Susumu, Owyang, Chung, Baba, Hiroshi, Fujimura, Masaki, Hamada, Eiji, Shimada, Tadahito, Kabemura, Teppei, Chijiiwa, Yoshiharu, Sato, T., Koito, K., Matsuda, Hiroko, Kawasaki, Tsunehisa, Obara, Katsutoshi, Kasukawa, Reiji, Miyoshi, Hirofumi, Matsumoto, Akio, Yamamoto, Manabu, Ohmasa, Ryouji, Kokubu, Shigehiro, Shibata, Hisao, Tajiri, Takashi, Onda, Masahiko, Hashizume, Makoto, Sugimachi, Keizo, Kobayashi, Kenji, Shiozaki, Hitoshi, Fujisaki, Junko, Shimoda, Tadakazu, Hase, Satoshi, Tsukamoto, Yoshihisa, Atsumi, M., Konishi, H., Nakajo, Shinobu, Fujiyama, Yoshihide, Taruishi, Masaki, Ayabe, Tokiyoshi, Morise, Kimitomo, Yamaguchi, Takeo, Makiyama, Kazuya, Itsuno, Minoru, Matsui, T., Okabe, N., Okabe, Nobuo, Matsui, Toshiyuki, Sakatani, Arata, Koizumi, Koichi, Imai, Yutaka, Sugino, Yoshinori, Masaki, Tadahiko, Sawada, Toshio, Nishigami, Takashi, Satomi, Masamichi, Hatada, Yasumasa, Saito, Hiroshi, Kobayshi, Kiyonori, Katsumata, Tomoe, Sugimoto, Kenji, Itabashi, Tsukasa, Kitagawa, Motoji, Hayakawa, Tetsuo, Okazaki, Kazuichi, Yamamoto, Yasuro, Funakoshi, Akihiro, Miyasaka, Kyoko, Soejima, Kazuhiko, Kanda, Mikio, Sugiyama, Masanori, Kuroda, Akira, Inoue, Hisayuki, Bamba, Tadao, Hamanaka, Y., Suzuki, T., Suzuki, Mamoru, Hanyu, Fujio, Tamura, Katsuhiro, Nakase, Akira, Noguchi, M., Hiwatashi, N., Murata, Yuhji, Suzuki, Kazuo, Ohtani, Haruo, Watanabe, Yoshihisa, Zeniya, Mikio, Aizawa, Yoshio, Masumoto, T., Onji, M., Hamasaki, Keisuke, Nakata, Keisuke, Fukui, Hiroshi, Tsujii, Tadasu, Yamashiki, Masayoshi, Nishimura, Akira, Tsutsui, Hiroko, Mizoguchi, Yasuhiro, Kimura, Fumio, Miyazaki, Masaru, Kiyota, Keisuke, Inokuchi, Hideto, Yamamoto, Yoshihiro, Oka, Hiroshi, Horikoshi, Tsutomu, Sekiguchi, Toshikazu, Takayasu, H., Shirai, T., Hongo, Michio, Okuno, Yo, Okano, H., Aoyama, N., Ohsuki, Masao, Maeda, Kenji, Haruma, Ken, Sumii, Koji, Nakai, Yoshihide, Fukunaga, Mikihiko, Kaneko, Hiroshi, Morise, Kimitomo, Okumura, Toshikatsu, Uehara, Akira, Fukuda, Yoshihiro, Satomi, Masamichi, Joh, Takashi, Itoh, Makoto, Kitagawa, Yuko, Kitajima, Masaki, Iwao, Tadashi, Toyonaga, Atsushi, Nakamura, Masahiko, Oda, Masaya, Kawamura, Yukimitsu, Dohden, Kenji, Kamiyama, Yasuhiko, Matsuno, Seiki, Hirano, Morihisa, Otsuka, Sachio, Ito, Masahiro, Sekine, Ichiro, Ogihara, Tatsuo, Sato, Nobuhiro, Uehara, Akira, Namiki, Masayoshi, Sugiura, Nobuyuki, Ebara, Masaaki, Matsuo, Naoki, Uchida, Hideo, Okada, Shuichi, Okazaki, Nobuo, Tsujii, Hirohiko, Ohsuga, Toshiaki, Abe, M., Nagata, Y., Yamasaki, Susumu, Kosuge, Tomoo, Kitamoto, Mikiya, Nakanishi, Toshio, Ichikawa, Yuzo, Mizoguchi, Yasuhiro, Ohtake, Yoshio, Hirasawa, Hiroyuki, Sugihara, Junichi, Muto, Yasutoshi, Yasunaga, Mitsuru, Okita, Kiwamu, Ukida, Minoru, Tsuji, Takao, Isai, Hideya, Uchino, Junichi, Suzuki, Katsuhiko, Komatsu, Kanji, Ohtomo, Yumiko, Idezuki, Yasuo, Sakuramachi, Shunji, Kimura, Taizo, Kitano, Seigo, Sugimachi, Keizo, Moriyama, Masaaki, Yazaki, Yasuyuki, and Saito, Takashige

Published
1993
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35. WHICH INSCRIBED SPHERE OF PYRAMIDS IS MAXIMAL?

Author

Kamiyama, Yasuhiko

Abstract

Consider the following question: In a circular cone, with bus line having length 1, the inscribed sphere is to be maximal. How much is the radius of the base circle? It is easy to see that the answer is (√-1)/2, which is interesting because this is the reciprocal of the golden section. In this paper, we generalize the question to the case that the base circle is generalized to regular polygons., 紀要論文

Published
2014

36. AN EXTREMAL VALUE PROBLEM CONCERNING THE INSCRIBED SPHERE OF PYRAMIDS

Author

Kamiyama, Yasuhiko

Abstract

Consider the following question: In a circular cone, with the sum of the radius of the base circle and the length of the bus line being 1, the inscribed sphere is to be maximal. How much is the radius of the base circle? It is easy to see that the answer is 1/3, which is geometrically interpreted as follows: Consider the section of a cone by a plane which contains the apex and is perpendicular to the base circle. Then the answer corresponds to the case that the section is an equilateral triangle. In this paper, we generalize the question to the case that the base circle is generalized to regular polygons., 紀要論文

Published
2014

41. The mapping degree of a diffeomorphism between polygon spaces

Author

Kamiyama, Yasuhiko

Subjects
Mathematics::Operator Algebras, Mathematics::Rings and Algebras
Abstract

Let M_n be the moduli space of equilateral polygon linkages with n vertices, each edge having length 1 in the Euclidean plane R^2 modulo orientation preserving isometry group of R^2. For a given diffeomorphism φ:M_n→M_n, we give a method to determine whether φ preserves the orientation or not. We also determine H_*(M_n/φ;Q) when φ is a certain involution., 紀要論文

Published
2013

42. Remarks on the homology of a regular 2-cover

Author

Kamiyama, Yasuhiko

Abstract

Let p: X→Y be a regular 2-cover. We assume that the group H_*(X;Z) are torsion free. It is easy to show that H_* (X;Z) are odd-torsion free. It is also well-known that the torsion subgroup of H_*(X;Z) has exponent 2. Several applications are also known. Since the results are scattered and somehow hidden in the literature, a survey of these researches may be useful. This is the purpose of this note. Our applications include the study of the homology of planar polygon space., 紀要論文

Published
2013

43. An exotic involution on the moduli space of planar polygons

Author

Kamiyama, Yasuhiko

Abstract

Let M_n be the moduli space of equilateral polygon linkages with n vertices, each edge having length 1 in the Euclidean plane R^2 modulo SO(2)⋉R^2, the orientation preserving isometry group of R^2. The space M_n admits the well-known involution, that is, the reflection about the x-axis. In this paper, we consider the reflection about the y-axis. We determine the rational homology groups of the orbit space., 紀要論文

Published
2013

44. THE RIEMANNIAN VOLUME OF THE MODULI SPACE OF PLANAR QUASI-EQUILATERAL POLYGONS WITH VERTEX NUMBER 4, 5 OR 6

Author

KAMIYAMA, YASUHIKO

Abstract

Let P(n, r) be the moduli space of n-gons in R^2 whose edge lengths are 1, ... , 1 and r. There is an inclusion P(n, r) → (R^2)^n. Restricting the usual Riemannian metric on (R^2)^n, we regard P(n, r) as a Riemannian manifold. In this paper, with the aid of a computer, we compute the volume of P(n, r) for n = 4, 5 and 6., 紀要論文

Published
2012

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