Kouki Taniyama   [Japanese Page]

Presentation slide 20200124


Site-specific Gordian distances of spatial graphs, to appear in J. Knot Theory Ramifications. (arXiv:1703.09440)

Achiral 1-cusped hyperbolic 3-manifolds not coming from amphicheiral null-homologous knot complements, Lobachevskii Journal of Mathematics, 39 (2018), no. 9, 1353-1361. (with Authors: K. Ichihara and I. Jong) (arXiv:1709.09418)

Stick number of tangles, J. Knot Theory Ramifications, 26 (2017), no. 13, 1750094, 9 pp. (with Y. Huh and J. Lee)

Circle arrangements of link projections, Kobe J. Math., 34 (2017), no. 1-2, 27–36. (with N.
Ito and S. Matsuzaki)

Strong and weak (1,3) homotopies on knot projections, Osaka J. Math., 52 (2015), no. 3, 617-646. (with
N. Ito and Y. Takimura)

Discontinuous maps whose iterations are continuous, Nihonkai Math. J., 25 (2014), no. 2, 119-125.(

Mapping a knot by a continuous map, J. Knot Theory Ramifications, 23 (2014), no. 10, 1450052, 14 pp.(arXi:1409.0399

Plane curves in an immersed graph in $R^2$, J. Knot Theory Ramifications, 22 (2013) 1350003 (2013) [10 pages] DOI: 10.1142/S021821651350003X (with M. Sakamoto) (

Multiplicity of a space over another space, J. Math. Soc. Japan, Vol. 64, No. 3 (2012), 823-849.(

$\triangle Y$-exchanges and the Conway-Gordon theorems, J. Knot Theory Ramifications, 21 (2012), No. 7, 1250067. (with R. Nikkuni)(

On intrinsically knotted or completely 3-linked graphs, Pacific J. Math., Vol. 252, No. 2, (2011), 407-425. (with R. Hanaki, R. Nikkuni, and A. Yamazaki)(

Braid presentation of spatial graphs, Tokyo J. Math. 33 (2010), no. 2, 509-522. (with K. Kanno) (arXiv:0901.1511)

Almost positive links have negative signature,
J. Knot Theory Ramifications, Vol. 19, No. 2 (2010), 187–289. (with J. Przytycki)(arXiv:0904.4130

A graph-theoretic approach to a partial order of knots and links, Topology Appl., 157 (2010), 1002–1010. (with T. Endo and T. Itoh) (arXiv:0806.3595)

Circle immersions that can be divided into two arc embeddings, Proc. Amer. Math. Soc. 138 (2010), 743-751. (

Symmetries of spatial graphs and Simon invariants, Fund. Math. 205 (2009), 219-236. (with R. Nikkuni) (arXiv:0708.0066)

Unknotting numbers of diagrams of a given nontrivial knot are unbounded,
J. Knot Theory Ramifications, 18 (2009), no. 8, 1049-1063. (arXiv:0805.3174)

An irreducible rectangle tiling contains a spiral, Journal of Geometry, 90 (2008), 175-184. (with T. Motohashi)
pdf file

2-irreducibility of spatial graphs,
J. Knot Theory Ramifications, 15 (2006), no. 1, 31-41. (with F. Lei and G. Zhang) pdf file

Newly found forbidden graphs for trivializability,
J. Knot Theory Ramifications, 14 (2005), no. 4, 523-538. (with R. Nikkuni, M. Ozawa, and Y. Tsutsumi)  pdf file

Identifiable projections of spatial graphs,
J. Knot Theory Ramifications, 13 (2004), no. 8, 991-998. (with Y. Huh) pdf file

A large complete graph in a space contains a link with large link invariant,
J. Knot Theory Ramifications, Vol. 12, No. 7 (2003), 915-919. (with M. Shirai) pdf file

Homology classification of spatial graphs by linking numbers and Simon invariants, Topology Appl., vol. 134, 53-67, (2003). (with R. Shinjo)
pdf file

Local moves on spatial graphs and finite type invariants, Pacific J. Math., vol. 211, 183-200, (2003). (with A. Yasuhara)

Band description of knots and Vassiliev invariants, Math. Proc. Cambridge Philos. Soc., 133 (2002), no. 2, 325-343. (with A. Yasuhara)

Clasp-pass moves on knots, links and spatial graphs, Topology and its Applications, 122 (2002), no. 3, 501-529. (with A. Yasuhara)

Realization of Vassiliev invariants by unknotting number one knots, Tokyo J. Math., 25 (2002), no. 1, 17-31. (with Y. Ohyama and S. Yamada)

Dividing a topological space into mutually disjoint and mutually homeomorphic subspaces, Topology and its Applications, 122 (2002), 421-423.

Irreducibility of spatial graphs,
J. Knot Theory Ramifications, 11, (2002), 121-124. pdf file

Vassiliev invariants of knots in a spatial graph, Pacific Journal of Mathematics,  200 (2001), 191-205. (with Y. Ohyama)

The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings. Proc. Amer. Math. Soc. 129 (2001), 2799-2802. (with J. Przytycki)

Realization of knots and links in a spatial graph, Topology Appl. 112 (2001), no. 1, 87--109. (with A. Yasuhara)

Higher dimensional links in a simplicial complex embedded in a sphere, Pacific J. Math. 194 (2000), no. 2, 465-468.

Regular projections of knotted handcuff graphs,
J. Knot Theory Ramifications, 7 (1998), 509-517. (with C. Yoshioka)

Total curvature of graphs in Euclidean spaces, Differential Geometry and its Applications, 8, (1998), 135-155.

Knotted subgraphs in a spatial graph, Kobe Journal of Mathematics, 14 (1997), 207--212.

Delta unknotting operation and vertex homotopy of graphs in $R^3$, Proceedings of Knots 96 Tokyo, (S. Suzuki ed.), World Scientific Publ. Co., (1997), 185-200. (with T. Motohashi)

Knot-inevital projections of planar graphs,
J. Knot Theory Ramifications, 5 (1996), 877-883. (with T. Tsukamoto)

Homology classification of spatial embeddings of a graph, Topology and its Applications, 65 (1995), 205-228.

Knotted projections of planar graphs, Proceedings of the American Mathematical Society, 123, (1995), 3575-3579.

On $C$-distance of knots, Kobe Journal of Mathematics, 11, (1994), 117-127. (with A. Yasuhara)

Yamada polynomial and crossing number of spatial graphs, Revista Matematica de la Universidad Complutense de Madrid, 7, (1994), 247-277. (with T. Motohashi and Y. Ohyama)

Cobordism, homotopy and homology of graphs in $R^3$, Topology, 33, (1994), 509-523.

Link homotopy invariants of graphs in $R^3$, Revista Matematica de la Universidad Complutense de Madrid, 7, (1994), 129-144.

Cobordism of theta curves in $S^3$, Mathematical Proceedings of Cambridge Philosohical Society, 113, (1993), 97-106.

On unknotting operations of two-bridge knots, Mathematische Annalen, 291, (1991), 579-589.

Unknotting operations involving trivial tangles, Osaka Journal of Mathematics, 27, (1990), 555-566. (with J. Hoste and Y. Nakanishi)

A partial order of links, Tokyo Journal of Mathematics, 12, (1989), 475-484.

A partial order of knots, Tokyo Journal of Mathematics, 12, (1989), 205-229.

Kouki Taniyama
Department of Mathematics, School of Education, Waseda University