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15 votes
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Essential uniqueness of the real-analytic structure on $\mathbb R$

It is well-known that any $C^k$-smooth $1$-manifold homeomorphic to $\mathbb R$ is $C^k$-diffeomorphic to $\mathbb R$. The cases of $k\in{\mathbb N}\cup$ {$\infty$} may all be handled similarly by ...
Adam Epstein's user avatar
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3 votes
6 answers
1k views

Dolbeault cohomology

Hello I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?
Learner's user avatar
  • 143
6 votes
4 answers
2k views

Space of $(1,0)$-holomorphic forms on a Riemann surface

In a complex analysis course I have been given the following definition: Let $X$ be a Riemann surface, denote by $H(1,0)$ the space of all $(1,0)$-holomorphic forms on $X$ and consider the quotient ...
Learner's user avatar
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