New York Journal of Mathematics
Volume 21 (2015) 823-835


Masaharu Ishikawa, Thomas W. Mattman, and Koya Shimokawa

Tangle sums and factorization of A-polynomials

view    print

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

We show that there exist infinitely many examples of pairs of knots, K1 and K2, that have no epimorphism
π1(S3 \ K1)→ π1(S3 \ K2)
preserving peripheral structure although their A-polynomials have the factorization AK2(L,M)| AK1(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 A-polynomials, the converse generally fails.


The first author is supported by MEXT, Grant-in-Aid for Young Scientists (B) (No. 22740032). The third author is supported by the MEXT, Grant-in-Aid for Scientific Research (C) (No. 22540066).

Author information

Masaharu Ishikawa:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan

Thomas W. Mattman:
Department of Mathematics and Statistics, California State University, Chico, Chico CA 95929-0525, USA

Koya Shimokawa:
Department of Mathematics, Saitama University, Saitama 338-8570, Japan