# Tag Info

### Is my proof of the equation $d=dx^i\wedge \partial_i$ correct?

Regarding the title Actually the answer can be found in the book that I quoted: In my proof I used the defining properties of the differential, see theorem $2.53$. If we look at the proof of that ...
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### Reference request: bundle of holomorphic differentials over Teichmüller space

This is a very good question. I ran into the same issue some months ago, and found it very difficult to find a reference. I warmly recommend Bers' 1960 paper "Holomorphic Differentials as ...
• 4,616
1 vote
Accepted

### Generator of $H^1(S^1)$ via integration of a bump $1$-form on $S^1$

There is a map $$H^1(S^1) \to \mathbb{R}$$ given by $\omega \mapsto \int_{S^1} \omega$. A priori this might be the zero map, but they've proven that it isn't by constructing a closed one-form with ...
• 26.4k
Accepted

• 5,771

• 1,261
1 vote
Accepted

### Absolute value in pseudo Riemannian volume form

It's just not true that $\det(A)^2=\det(g)$ in general. Think of flat space $\mathbb{R}^{s,t}$ with signature $(s,t)$, with Cartesian coordinates and $A$ being the identity matrix. I'm not sure how ...
• 3,784
1 vote

### Derivative of identity map and moving forms

This discussion is confused. Tildes appear and then disappear. A $1$-form is scalar-valued, unless you specifically speak of a vector-valued $1$-form or, more generally, a $1$-form with values in a ...
• 103k

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