Open AccessOn Some Deformations of Riemann Surfaces. I
Author(s) -
Ryszard L. Rubinsztein
Publication year - 2000
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14288
Subject(s) - mathematics , infinitesimal , riemann surface , cohomology , pure mathematics , genus , riemann–hurwitz formula , riemann hypothesis , representation (politics) , riemann sphere , series (stratigraphy) , mathematical analysis , compact riemann surface , geometric function theory , paleontology , botany , politics , political science , law , biology
We define a family of infinitesimal deformations of compact Riemann surfaces of genus $g > 2$ which generalizes the Fenchel-Nielsen deformations. Those new deformations are associated to smooth vector fields on the circle. We compute a representation of the deformations in terms of Poincaré series and determine the corresponding Eichler cohomology classes.