TANAKA Toshifumi Last updated: Dec 12, 2018 at 03:49

Published Papers

結び目を用いた高専の学生向け数学教材の実践～ゲーリッツ不変量を通して～

Apr 2013

結び目を用いた中学生向け数学教材の実践

Apr 2012 [Refereed]

Positive knots and Rasmussen's invariant

Tanaka, Toshifumi

Apr 2013

An infinite family of prime satellite knots with the same Alexander polynomial

Tanaka, Toshifumi

Apr 2012

Tanaka, Toshifumi

Apr 2011 [Refereed]

Misc

Toshifumi Tanaka

Journal of Knot Theory and its Ramifications 20 1229-1236

By using Rasmussen's s-invariant derived from Khovanov homology, we give a combinatorial proof for the existence of countably many Casson handles. © 2011 World Scientific Publishing Company.

Toshifumi Tanaka

Proceedings of the American Mathematical Society 127(11) 3427-3432 Dec 1999

By using results of Yamada and of Yokota, concerning link diagrams and link polynomials, we give some relationships between maximal Bennequin numbers and Kauffman polynomials of positive links. © 1999 American Mathematical Society.

Toshifumi Tanaka

Topology and its Applications

© 2015 Elsevier B.V. As a consequence of Donaldson's result, concerning the intersection forms of smooth 4-manifolds, we show that there exists an exotic smooth structure on {music sharp sign}∞CP2.

Toshifumi Tanaka

Topology and its Applications 180 132-141

© 2014 Elsevier B.V. It is known that there does not exist a Legendrian embedding of K4 such that all its cycles realize the maximal Thurston-Bennequin numbers that only consist of odd numbers. This paper represents an infinite family of spatial g...

Toshifumi Tanaka

Journal of the Korean Mathematical Society 52 389-402

© 2015 Korean Mathematical Society. A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are sym- metric with respect to an axis in the 2-plane, by connecting them with 2-tangles wit...

Research Grants & Projects

Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(若手研究(B))

Project Year: 2011 - 2013 Investigator(s): Toshifumi TANAKA

In a mathematical investigation of knots, some studies for a classification of a knot and its application were done by using algebraic and topological methods. As a result, a relationship between given two knots has been investigated by using item...

Study on quantum invariants using skein theory and representation of fundamental groups

Project Year: 2004 - 2007

Knot homologies and smooth structure of 4-dimensional manifolds

Project Year: 2006

We investigate smooth structure of 4-dimensional manifolds by using knot theory

Japan Society for the Promotion of Science: Grants-in-Aid for Scientific Research

Project Year: Apr 2005 - Mar 2007