# Tagged Questions

**19**

votes

**6**answers

3k views

### Is there a preferable convention for defining the wedge product?

There are different conventions for defininig the wedge product $\wedge$.
In Kobayashi-Nomizu, there is $\alpha\wedge\beta:=Alt(\alpha\otimes\beta)$,
in Spivak, we find ...

**1**

vote

**1**answer

234 views

### Commutativity of pullbacks and the exterior derivative as an unbounded operator on $L^2$

Let $d_c, \delta_c$ be operators with domains $D(d_c) = D(\delta_c) = C_{c}^\infty(\wedge T^\ast M)$. We let $d_c$ be the usual exterior derivative on compactly supported smooth forms, ie., $d_c\omega ...

**3**

votes

**0**answers

218 views

### Density of C^\infty in the domain of the exterior derivative on a noncompact, complete manifold?

Let $(M,g)$ be a geodesically complete Riemannian manifold that is not necessarily compact. Futhermore, assume that $M$ has at most exponential volume growth (ie., locally doubling property). Let ...