 

Masaharu Ishikawa, Thomas W. Mattman, and Koya Shimokawa
Tangle sums and factorization of Apolynomials view print


Published: 
August 27, 2015 
Keywords: 
A polynomial, knot group, tangle sum 
Subject: 
57M25 


Abstract
We show that there exist infinitely many examples of pairs of knots, K_{1} and K_{2},
that have no epimorphism
π_{1}(S^{3} \
K_{1})→
π_{1}(S^{3} \ K_{2})
preserving peripheral structure although their Apolynomials have the factorization
A_{K2}(L,M) A_{K1}(L,M).
Our construction accounts for most of the known factorizations of this form
for knots with 10 or fewer crossings.
In particular, we conclude that
while an epimorphism will lead to a factorization of Apolynomials,
the converse generally fails.


Acknowledgements
The first author is supported by MEXT, GrantinAid for Young Scientists (B) (No. 22740032). The third author is supported by the MEXT, GrantinAid for Scientific Research (C) (No. 22540066).


Author information
Masaharu Ishikawa:
Mathematical Institute, Tohoku University, Sendai 9808578, Japan
ishikawa@math.tohoku.ac.jp
Thomas W. Mattman:
Department of Mathematics and Statistics, California State University, Chico, Chico CA 959290525, USA
TMattman@CSUChico.edu
Koya Shimokawa:
Department of Mathematics, Saitama University, Saitama 3388570, Japan
kshimoka@rimath.saitamau.ac.jp

