Quantum extensions of ordinary maps
作者: Andre Kornell
刊名: Proceedings of the American Mathematical Society, 2020, Vol.148 (5), pp.1971-1986
来源数据库: American Mathematical Society Journal
DOI: 10.1090/proc/14851
原始语种摘要: We define a loop to be quantum nullhomotopic if and only if it admits a nonempty quantum set of extensions to the unit disk. We show that the canonical loop in the unit circle is not quantum nullhomotopic, but that every loop in the real projective plane is quantum nullhomotopic. Furthermore, we apply Kuiper's theorem to show that the canonical loop admits a continuous family of extensions to the unit disk that is indexed by an infinite quantum space. We obtain these results using a purely topological condition that we show to be equivalent to the existence of a quantum family of extensions of a given map.
全文获取路径: AMS 

  • projective 投射的
  • quantum 量子
  • topological 拓扑的
  • canonical 标准的
  • circle 
  • apply 应用
  • ordinary 普通的
  • continuous 连续的
  • purely 纯粹地
  • infinite 无穷的