International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 695-708
On monodromy map
Department of Mathematics and Computer Science, Elizabeth City State University, Elizabeth City 27909, NC, USA
Received 2 April 1992; Revised 22 September 1992
Copyright © 1993 Jharna D. Sengupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a Fuchsian group acting on the upper half-plane and having signature
Let be the Teichmüller space of . Then there exists a vector bundle of rank
over whose fibre over a point representing is the space of bounded
quratic differentials for . Let be the set of all homomorphisms from into
the Mbius group .
For a given we get an equivalence class of projective structures and a
conjugacy class of a homomorphism . Therefore there is a well defined map
is called the monodromy map. We prove that the monromy map is
hommorphism. The case gives the previously known result by Earle, Hejhal