Dynamics of Teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type

2018 ◽  
Vol 12 (1) ◽  
pp. 1-64
Author(s):  
Katsuhiko Matsuzaki
Keyword(s):  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Infinite Type ◽  
And Topology ◽  
Modular Groups

scholarly journals Moduli spaces of isoperiodic forms on Riemann surfaces

2014 ◽  
Vol 163 (12) ◽  
pp. 2271-2323 ◽  
Author(s):  
Curtis T. McMullen
Keyword(s):  
Moduli Spaces ◽  
Riemann Surfaces

GEOMETRY OF THE MODULI SPACES OF HARMONIC MAPS INTO LIE GROUPS VIA GAUGE THEORY OVER RIEMANN SURFACES

2001 ◽  
Vol 12 (03) ◽  
pp. 339-371
Author(s):  
MARIKO MUKAI-HIDANO ◽  
YOSHIHIRO OHNITA
Keyword(s):  
Critical Point ◽  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Energy Function ◽  
Riemann Surfaces ◽  
Symmetric Spaces ◽  
Harmonic Maps ◽  
Point Subset ◽  
Presymplectic Structure

This paper aims to investigate the geometry of the moduli spaces of harmonic maps of compact Riemann surfaces into compact Lie groups or compact symmetric spaces. The approach here is to study the gauge theoretic equations for such harmonic maps and the moduli space of their solutions. We discuss the S1-action, the hyper-presymplectic structure, the energy function, the Hitchin map, the flag transforms on the moduli space, several kinds of subspaces in the moduli space, and the relationship among them, especially the structure of the critical point subset for the energy function on the moduli space. As results, we show that every uniton solution is a critical point of the energy function on the moduli space, and moreover we give a characterization of the fixed point subset fixed by S1-action in terms of a flag transform.

scholarly journals On the geometry and topology of partial configuration spaces of Riemann surfaces

2017 ◽  
Vol 17 (2) ◽  
pp. 1163-1188 ◽  
Author(s):  
Barbu Berceanu ◽  
Daniela Anca Măcinic ◽  
Ştefan Papadima ◽  
Clement Popescu
Keyword(s):  
Riemann Surfaces ◽  
Configuration Spaces ◽  
And Topology
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