论文标题
一致的交叉盖号码和结的理性跨度
The concordance crosscap number and rational Witt span of a knot
论文作者
论文摘要
一个结$ k $的一致性交叉盖数$γ_c（k）$是任何$ k'$的最小crosscap编号$γ_3（k'）$ concordant to $ k $（以及$γ_3（k'）$定义为最低的不可解决的表面$ en $ n norrientiantirientirentirentirentirentirentirentirentirent betti $ n norcement $ en $ s $ s $ s $ s $ s $张使用结决定因素和签名引入和研究了这种不变的，并已使用亚历山大多项式进行了进一步的研究。我们在这项工作中表明，结的理性witt类可用于通过一个新的整数价值不变的不变式来获得一致性交叉盖号码的下限，我们称之为结的witt spen。
The concordance crosscap number $γ_c(K)$ of a knot $K$ is the smallest crosscap number $γ_3(K')$ of any knot $K'$ concordant to $K$ (and with $γ_3(K')$ defined as the least first Betti number of any nonorientable surface $Σ$ embedded in $S^3$ with boundary $K'$). This invariant has been introduced and studied by Zhang using knot determinants and signatures, and has further been studied by Livingston using the Alexander polynomial. We show in this work that the rational Witt class of a knot can be used to obtain a lower bound on the concordance crosscap number, by means of a new integer-valued invariant we call the Witt span of the knot.
