典型文献
Free Cyclic Actions on Surfaces and the Borsuk-Ulam Theorem
文献摘要：
Let M and N be topological spaces,let G be a group,and let τ:G×M → M be a proper free action of G.In this paper,we define a Borsuk-Ulam-type property for homotopy classes of maps from M to N with respect to the pair(G,τ)that generalises the classical antipodal Borsuk-Ulam theorem of maps from the n-sphere Sn to Rn.In the cases where M is a finite pathwise-connected CW-complex,G is a finite,non-trivial Abelian group,τ is a proper free cellular action,and N is either R2 or a compact surface without boundary different from S2 and RP2,we give an algebraic criterion involving braid groups to decide whether a free homotopy class β∈[M,N]has the Borsuk-Ulam property.As an application of this criterion,we consider the case where M is a compact surface without boundary equipped with a free action τ of the finite cyclic group Zn.In terms of the orientability of the orbit space Mτ of M by the action τ,the value of n modulo 4 and a certain algebraic condition involving the first homology group of Mτ,we are able to determine if the single homotopy class of maps from M to R2 possesses the Borsuk-Ulam property with respect to(Zn,τ).Finally,we give some examples of surfaces on which the symmetric group acts,and for these cases,we obtain some partial results regarding the Borsuk-Ulam property for maps whose target is R2.
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中图分类号：
作者姓名：
Daciberg Lima GON?ALVES;John GUASCHI;Vinicius Casteluber LAASS
作者机构：
Departamento de Matemática,IME,Universidade de S?o Paulo,Rua do Mat?o 1010 CEP:05508-090,S?o Paulo-SP,Brazil;Normandie Univ.,UNICAEN,CNRS,LMNO,14000 Caen,France;Universidade Federal da Bahia,IME,Departamento de Matemática,Av.Milton Santos,S/N Ondina CEP:40170-110,Salvador-BA,Brazil
文献出处：
引用格式：
[1]Daciberg Lima GON?ALVES;John GUASCHI;Vinicius Casteluber LAASS-.Free Cyclic Actions on Surfaces and the Borsuk-Ulam Theorem)[J].数学学报（英文版）,2022(10):1803-1822
A类：
Borsuk,generalises,antipodal,pathwise,orientability
B类：
Free,Cyclic,Actions,Surfaces,Ulam,Theorem,Let,topological,spaces,let,free,action,In,this,paper,we,define,type,property,homotopy,classes,maps,from,respect,pair,that,classical,theorem,sphere,Sn,Rn,cases,where,finite,connected,CW,complex,trivial,Abelian,cellular,either,compact,without,boundary,different,S2,RP2,give,algebraic,criterion,involving,braid,groups,decide,whether,has,application,consider,equipped,cyclic,terms,orbit,by,value,modulo,certain,condition,first,homology,are,able,determine,single,possesses,Finally,some,examples,surfaces,which,symmetric,acts,these,obtain,partial,results,regarding,whose,target
AB值：
0.452221
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