2005 Fiscal Year Final Research Report Summary

Computer Aided Knot Theory on Linux

Research Project

Project/Area Number	15540072
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Geometry
Research Institution	NARA WOMEN'S UNIVERSITY
Principal Investigator	OCHIAI Mitsuyuki Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (70016179)
Co-Investigator(Kenkyū-buntansha)	KAKO Fujio Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (90152610)
Project Period (FY)	2003 – 2005
Keywords	Linux / knot / tangle / base tangle / polynomial invariant / mutant / Hecke algebras
Research Abstract	(1)We made Matrix representations of Hecke algebras H(q,n) of n up to 18. (2)We made a computer program bTd to assist knot researchers about the followings : (2.1) to compute base tangle decompositions of n-tangles with 1<n<10. (2.2) to compute HOMELY polynomials of knots and links using tangle decompositions (3)HEAD INVESTIGATOR writes a paper "Base Tangle Decompositions of n-string tangles with 1<n<10" submitted to Experimental Mathematics (4)We had founded two mutant knots K1 and K2 with 12 crossings such that P(K1^3;x,y) equals to P(K2^3;x,y) but P(K1^4;x,y) does not equal to P(K2^4 ;x,y). (5)Our software bTd had been opened at http://amadeus.ics.nara-wu.ac.jp/~ochiai/

(6 results)