Let be the surface group of genus , and denote by the space of the homomorphisms from into the group of the orientation preserving homeomorphisms of . Let for some positive integers and . Then the subset of formed by those which are semiconjugate to -fold lifts of some homomorphisms and which have Euler number is shown to be clopen. This leads to a new proof of the main result of Kathryn Mann [Man] from a completely different approach.
Cite this article
Shigenori Matsumoto, Basic partitions and combinations of group actions on the circle: A new approach to a theorem of Kathryn Mann. Enseign. Math. 62 (2016), no. 1/2, pp. 15–47DOI 10.4171/LEM/62-1/2-4