$A_\infty$代数族与同伦群作用
Families of $A_\infty$ algebras and homotopy group actions
摘要：
定义了以流形M为索引的$A_\infty$代数族的同伦群作用。我们给出了流形上由一条路诱导的$A_\infty$态射和同伦路对所对应的$A_\infty$同伦的显式公式。最后，我们计算有限群和非交换群的例子，并确定每个同伦群作用的有限群是同伦的严格群作用。
英文摘要：
We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a pair of homotopic paths. Finally, we compute examples for finite groups and finitely generated free nonabelian groups and determine that every homotopy group action by a finite group is homotopic to a strict group action.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
