标题： Klein瓶上2-值非分裂映射的Nielsen不动点数的计算 显示英文标题

标题： Computation of the Nielsen fixed point number for 2-valued non-split maps on the Klein bottle

摘要： 本文研究了取值为2的非分裂映射，重点关注 Klein 瓶。 我们建立了取值为2的非分裂映射$\phi:X\multimap Y$和一对映射类$([f],[f\circ \delta])\in [\tilde X,Y]\times[\tilde X, Y]$之间的联系，其中$\delta$是$\tilde X$上的一个自由对合变换，而$X=\tilde X/\delta$和提升因子类$[f]$在相对于$\delta$时，不满足 Borsuk-Ulam 性质。 我们还展示了一种方法，可以计算闭合连通流形上的取值为2的非分裂映射的 Nielsen 不动点数，该方法通过提升因子与覆盖空间映射之间的 Nielsen 共定点数来表示，并将公式从仅适用于可定向流形推广到也包括不可定向流形的情况。 最后，我们给出了 Klein 瓶上取值为2的非分裂映射的 Nielsen 不动点数的公式，该公式用 Klein 瓶上的两个辫子表示。 显示英文摘要

摘要： In this paper we study 2-valued non-split maps, focusing on the Klein bottle. We establish a connection between a 2-valued non-split map $\phi:X\multimap Y$ and a pair of classes of maps $([f],[f\circ \delta])\in [\tilde X,Y]\times[\tilde X, Y]$, where $\delta$ is a free involution on $\tilde X$, $X=\tilde X/\delta$ and the class of the lift factor $[f]$ does not satisfy the Borsuk-Ulam Property in respect to $\delta$. We also exhibit a method to compute the Nielsen fixed point number of a 2-valued non-split map on a closed connected manifold in terms of the Nielsen coincidence number between a lift factor and a covering space map, generalizing the formula from only orientable manifolds to also non-orientable manifolds. Finally we display a formula for the Nielsen fixed point number of 2-valued non-split maps on the Klein bottle in terms of two braids of the Klein bottle.