Chennai Mathematical Institute

Seminars




3.30 pm, Seminar Hall
Generators of the Mapping Class Group of a surface of genus g (Research seminar talk for MSc Maths)

Neetal Neel
MSc Maths, Chennai Mathematical Institute.
11-10-17


Abstract

In the early 1960's Lickorish proved that the Mapping Class Group is generated by Dehn twists about 3g-1 non-separating simple closed curves on a genus g surface. Humphries later reduced the number to 2g+1 and proved it to be the minimal number required to generate the mapping class group using only Dehn twists. In the first part of the talk I will describe the basic concepts of Dehn twists and the Mapping Class Group. In 2004, Tara Brendle and Benson Farb proved that the Mapping Class Group can be generated by 3 torsion elements. Moreover they proved that the Mapping Class Group can be generated by 6 involutions. In the second part of the talk I will explain how to get to these results.





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