Odd-homology thickness conjecture for mixed rational-tangle algebraic links

Let pip_i and qjq_j be positive rational tangles not starting with 11, and consider (p1,,pm)(q1,,qn)(p_1,\ldots,p_m)(q_1,\ldots,q_n-). Assume the tangles are not all integer. Let pi\overline p_i and qj\overline q_j be their reductions, and put q=min(q1,,qn)q=\min(\overline q_1,\ldots,\overline q_n).

Mixed-tangle thickness conjecture. The link is Kh\overline{Kh}'-thick if m3m\ge3, q>1q>1, each pip_i of length at least 22 satisfies pi=1\overline p_i=1, and

max(p1,p2,,pm)q.\max(\overline p_1,\overline p_2,\ldots,\overline p_m)\le q.

This extends the preceding integer-tangle criterion to mixed rational tangles. The supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Slavik Jablan and Radmila Sazdanović, “Quasi-alternating links and odd homology: computations and conjectures”, arXiv:0901.0075 (2014).

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