| |
|
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 |
|
|
Abstract
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.
|
|
| Acknowledgements
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
ishikawa@math.tohoku.ac.jp
Thomas W. Mattman:
Department of Mathematics and Statistics, California State University, Chico, Chico CA 95929-0525, USA
TMattman@CSUChico.edu
Koya Shimokawa:
Department of Mathematics, Saitama University, Saitama 338-8570, Japan
kshimoka@rimath.saitama-u.ac.jp
|
|
