Knot projections with reductivity two

Noboru Ito*, Yusuke Takimura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Reductivity of knot projections refers to the minimum number of splices of double points needed to obtain reducible knot projections. Considering the type and method of splicing (Seifert type splice or non-Seifert type splice, recursively or simultaneously), we can obtain four reductivities containing Shimizu's reductivity, three of which are new. In this paper, we determine knot projections with reductivity two for all four of the definitions. We also provide easily calculated lower bounds for some reductivities. Further, we detail properties of each reductivity, and describe relationships among the four reductivities with examples.

Original languageEnglish
Pages (from-to)290-301
Number of pages12
JournalTopology and its Applications
Publication statusPublished - 2015 Sept 5
Externally publishedYes


  • Knot projection
  • Reductivity
  • Spherical curve

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'Knot projections with reductivity two'. Together they form a unique fingerprint.

Cite this