Non-hyperbolic solutions to tangle equations involving composite links
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS(2021)
摘要
Solving tangle equations is deeply connected with studying enzyme action on DNA. The main goal of this paper is to solve the system of tangle equations N(O + X-1) = b(1) and N(O + X-2) = b(2)#b(3), where X-1 and X-2 are rational tangles, and b(i) is a 2-bridge link, for i = 1, 2, 3, with b(2) and b(3) nontrivial. We solve this system of equations under the assumption (O) over tilde, the double branched cover of O, is not pi-hyperbolic, i.e. O is not phyperbolic. Besides, we also deal with tangle equations involving 2-bridge links only under the assumption O is an algebraic tangle.
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关键词
DNA topology, tangle equations, Dehn surgery
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