Princeton University Press eBooks· 2015· Book chapter
On Compact Analytic Surfaces
- 740citations
- 2015year
Short summary
This abstract introduces a mathematical framework for classifying analytic fibre spaces, specifically focusing on compact analytic surfaces and their equivalences.
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Key points
- Defines a family of analytic fibre spaces $\mathcal{G}(\mathcal{A}, \Omega(B^\#))$ for compact analytic surfaces.
- Establishes that fibre space equivalences depend on the sheaf of structure groups.
- Introduces the concept of (\mathcal{G}-equivalence for fibre spaces.
- Identifies a cohomology class $c \in H^1(A, \mathcal{F}(B^\#))$ representing the $\Omega(B_i)$-equivalence class of $B_i$.
AI-generated from the title and abstract; the full text is not read.
Abstract
THEOREM 11.1. The family 9(,{, G) consists of all analytic fibre spaces Bi, '2C H'(A, f2(B#)). The notion of fibre spaces and their equivalences depends on the sheaf of structure groups.' By a (63-fibre space we mean a fibre space with a sheaf (3 of structure groups, and we say that two fibre spaces are (X-equivalent if they are equivalent as (63-fibre spaces. The fibre space Bi may be considered as an analytic fibre space, as an f2(BO)-fibre space, or as an f2(Bl)-fibre space. The cohomology class C) C H'(Ay, f(BO)) represents the f2(Bl)-equivalence class of Be. Let C& denote the fibre of BI over u c A. It is clear that
The authors' abstract, as published at the source. Princeton University Press eBooks, 2015 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics