TANAKA Toshifumi

J-GLOBAL         Last updated: Dec 12, 2018 at 03:49
TANAKA Toshifumi
Gifu University
Faculty of Education

Research Areas


Published Papers

   Apr 2013
   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


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 knot cobordism
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