Strong coprimality and strong irreducibility of Alexander polynomials |
| |
Authors: | Evan M BullockChristopher William Davis |
| |
Institution: | Rice University, Department of Mathematics, Houston, TX, United States |
| |
Abstract: | A polynomial f(t) with rational coefficients is strongly irreducible if f(tk) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(tk) and g(tl) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility and prove that the Alexander polynomials of twist knots are pairwise strongly coprime and that most of them are strongly irreducible. We apply these results to describe the structure of the subgroup of the rational knot concordance group generated by the twist knots and to provide an explicit set of knots which represent linearly independent elements deep in the solvable filtration of the knot concordance group. |
| |
Keywords: | Knot theory Knot concordance Ramification and extension theory |
本文献已被 ScienceDirect 等数据库收录! |