Universal Teichmüller space as a non-trivial example of infinite-dimensional complex manifolds

2020 ◽  
pp. 195-213
Author(s):  
Armen Sergeev
Keyword(s):  
Complex Manifolds ◽  
Infinite Dimensional

scholarly journals The Non-Vanishing of First Cohomology Groups for Certain Infinite-Dimensional Complex Manifolds

2005 ◽  
Vol 12 (1) ◽  
pp. 11-13
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundle ◽  
Complex Space ◽  
Holomorphic Vector Bundle ◽  
Banach Manifold ◽  
Complex Manifolds ◽  
Cohomology Groups ◽  
Large Classes ◽  
Infinite Dimensional

Abstract Here, using the ideas of an old paper by S. Dineen (An. Acad. Brasil. Ci. 48: 11–12, 1976), we give large classes of pairs (𝑋, 𝐸) such that 𝑋 is an infinite-dimensional complex space very far from a Banach manifold, 𝐸 is a holomorphic vector bundle on 𝑋 and 𝐻1(𝑋,𝐸) is infinite-dimensional.

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