Seminar on periods and motives | Rational K\pi 1 property for Reimann surfaces

Abstract：

In the study of mixed elliptic motives, we noticed the importance for rational K\pi 1 property on some bar complex arising from mixed elliptic motives. Since its bar complex is some what complicated, it will be useful to consider some easier case, the case for Riemann surfaces.

Rational fundamental group of Riemann surface is desribed by Sullivan's old paper, but it seems that rational K\pi 1 property seems to be not well discussed. As for arrangements of hyperplanes, several technic and results are know by several person, including the case for supersolvable case,etc.

In our talk, we consider some technic to show the rational K\pi 1 property for Riemann surfaces, which might be applicable to mixed elliptic motives.