# Questions tagged [smooth-manifolds]

For questions about smooth manifolds, a topological manifold with a maximal smooth atlas.

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### Smooth vector bundles over contractible smooth manifolds with or without boundary

First, let me just write down the definitions I will use (see e.g. Lee - Introduction to Smooth Manifolds): Two (real) vector bundles $(E,B,\pi)$ and $(E',B,\pi')$ (over the same base space $B$) are ...
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### Classification of smooth weak Fano three-folds

A variety is said to be 'weak Fano' or 'almost Fano' if its anti-canonical divisor is nef and big. In this question, let me restrict to the case of smooth varieties over the complex numbers. My ...
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### Sectional curvature and Ricci curvature are bounded away from $0$ on compact manifolds of positive curvature

I've seen this claim a few times and it made sense in my mind but I realize I don't really know how to fully justify it: Let $M$ be a compact Riemannian manifold with sectional curvature (resp. Ricci ...
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### Discreteness of branch points of a holomorphic map between Riemann surfaces [duplicate]

Let $X$ and $Y$ be Riemann surfaces (not necessarily compact) and $f:X\to Y$ a holomorphic map. A point $x\in X$ is said to be a ramificiation point of $f$ if the multiplicity of $f$ at $x$ is $\geq 2$...
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### Are the elements of $C^\infty(M)$ smooth functions or equivalence classes of functions?

I am familiar with the notation $C^\infty_p(M)$, which denotes the algebra of germs of $C^\infty$ functions at $p$, where two functions defined on a neighborhood of $p$ are equivalent if they agree on ...
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### Problem book recommendations on complex manifolds

I came across the book on Cauchy Riemann manifolds, "CR manifolds and tangential Cauchy Riemann complexes". The book does not have a problem section. I would be grateful if anyone recommends ...
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