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研究者リスト >> 髙瀨 将道
 

髙瀨 将道

 
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研究者氏名髙瀨 将道
所属成蹊大学
部署理工学部 共通基礎
職名教授
学位博士(数理科学)(東京大学大学院数理科学研究科)

研究キーワード

 
微分位相幾何学

研究分野

 
  • 数学 / 幾何学 / 
  • 数学 / 幾何学 / 

経歴

 
2007年4月
 - 
2011年3月
信州大学 理学部 准教授
 
2006年10月
 - 
2007年3月
信州大学 理学部 助教授
 

Misc

 
Naohiko Kasuya, Masamichi Takase
International Journal of Mathematics, Volume No.29, Issue No. 11, 2018      2018年3月
We show that, for a closed orientable n-manifold, with n not congruent to 3
modulo 4, the existence of a CR-regular embedding into complex (n-1)-space
ensures the existence of a totally real embedding into complex n-space. This
implies that a clos...
Naohiko Kasuya, Naohiko Kasuya, Masamichi Takase
Transactions of the American Mathematical Society   370 2023-2038   2018年1月
© 2017 American Mathematical Society. It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the 3-dimensional complex space. We show in fact that a 1-dimensional submanifold of a closed orientable 3-...
Masamichi Takase, Kokoro Tanaka
Mathematical Proceedings of the Cambridge Philosophical Society   161 237-246   2016年9月
Copyright © 2016 Cambridge Philosophical Society. For each diagram D of a 2-knot, we provide a way to construct a new diagram D′ of the same knot such that any sequence of Roseman moves between D and D′ necessarily involves branch points. The proo...
Kenji Daikoku, Keiichi Sakai, Masamichi Takase
Indiana University Mathematics Journal   61 1111-1127   2012年12月
For a knot diagramwe introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the st...
Yoshihiro Hirato, Masamichi Takase
Fundamenta Mathematicae   216 119-128   2012年4月
According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket i...
Masamichi Takase
Mathematische Zeitschrift   272 101-108   2012年1月
We give a formula to detect the oriented bordism class of a codimension one immersion of an oriented 7-manifold in terms of singularities of its singular Seifert surface, that is, a generic map from a compact 8-manifold which extends the given imm...
Tobias Ekholm, Masamichi Takase
Bulletin of the London Mathematical Society   43 251-266   2011年1月
A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self-intersection points equal to-n induces an immersion of the circle bundle over the 2-sphere of Euler class 2n into 4-space. Precomposing these circle bundle imme...
Dennis Roseman, Masamichi Takase
Algebraic and Geometric Topology   7 359-377   2007年12月
Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the 2-torus ...
Masamichi Takase, Masamichi Takase
Mathematische Zeitschrift   256 35-44   2007年5月
We show that for any given differentiable embedding of the three-sphere in six-space there exists a Seifert surface (in six-space) with arbitrarily prescribed signature. This implies, according to our previous paper, that given such a (6,3)-knot e...
Masamichi Takase, Masamichi Takase
Bulletin of the London Mathematical Society   39 39-45   2007年1月
We give a formula for the bordism class of an immersion of an oriented 3-manifold in 4-space. It expresses the class in terms of the topology of a null-cobordism of the 3-manifold and certain singularities (the number of umbilic points) of a gener...
Masamichi Takase
International Journal of Mathematics   17 869-885   2006年9月
For smooth embeddings of an integral homology 3-sphere in the 6-sphere, we define an integer invariant in terms of their Seifert surfaces. Our invariant gives a bijection between the set of smooth isotopy classes of such embeddings and the integer...
Masamichi Takase
Topology   43 1425-1447   2004年11月
Haefliger has shown that a smooth embedding of the (4k-1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in...
Osamu Saeki, András Szucs, Masamichi Takase
Manuscripta Mathematica   108 13-32   2002年12月
We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric formulae for t...
Osamu Saeki, Masamichi Takase
Transactions of the American Mathematical Society   354 5049-5061   2002年12月
We clarify the structure of the set of regular homotopy classes containing embeddings of a 3-manifold into 5-space inside the set of all regular homotopy classes of immersions with trivial normal bundles. As a consequence, we show that for a large...
Masamichi Takase
Pacific Journal of Mathematics   193 249-256   2000年3月
Let F : M 3 (Rightwards arrow with hook) R 5 be an embedding of an (oriented) Z 2 -homology 3-sphere M 3 in R 5 . Then F bounds an embedding of an oriented manifold W 4 in R 5 . It is well known that the signature σ(W 4 ) of W 4 is equal to t...

競争的資金等の研究課題

 
文部科学省: 科学研究費補助金(基盤研究(C))
研究期間: 2015年 - 2019年    代表者: 高瀬 将道
文部科学省: 科学研究費補助金(基盤研究(C))
研究期間: 2010年 - 2014年    代表者: 高瀬 将道
文部科学省: 科学研究費補助金(若手研究(B))
研究期間: 2007年 - 2010年    代表者: 高瀬 将道