题目：The Borsuk-Ulam type Theorem for maps from a surface to the  2-dimensional sphere. (joint work with John Guaschi and Vinicius Laass)

报告人:Daciberg Lima Goncalves    (圣保罗大学，巴西)

Abstract：We consider the set of maps $f: S/to S^2$ from a surface into the 2-sphere. For a given free involution $/tau$ on $S$ we classify which homotopy classes $/alpha$ have the property that for all $f/in /alpha$ we have that there is one orbit $/{x,/tau(x)$ such that $f(x)=f(/tau(x))$, where the point $x$ depends on the map $f$.

This is divided into three cases, namely I) The quotient $S//tau$ is orientable, II) $S$ orientable and  $S//tau$ non  orientable, III) $S$ non orientable. Then we consider the case where we have a free action of a cyclic group $Z_n$ on the surface $S$. In this situation the Borsuk-Ulam property is defined as  there is an orbit such that the image by $f$ has less than $n$ points. To show this result we make use of the homotopy fibre of the configuration space  into the product.

时间：4月18日（周四）下午2:30--3:30

地点：首都师大新教二楼513教室

联系人：赵学志

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