# Tagged Questions

**0**

votes

**1**answer

324 views

### Double tangent bundle of manifolds, two contradictory arguments

I am considering the double tangent bundle $T(TM)$ of manifolds $M$. Locally, if $M=R^d$ then $T(TM)=R^{4d}=\oplus^3 TM$. My attempt is to see whether $T(TM)\cong \oplus^3 TM$ naturally for any $M$. I ...

**7**

votes

**1**answer

494 views

### Is every graded manifold affine, and is this definition of graded manifold the right one?

The following definition is from:
Dmitry Roytenberg, "AKSZ-BV formalism and Courant algebroid-induced topological field theories", Letters in Mathematical Physics, 2007 vol. 79 (2) pp. 143-159, ...

**11**

votes

**2**answers

1k views

### Two fancy ways of defining differential forms: How does one show that they are equivalent?

Given a smooth manifold M, the following procedures yield the differential graded algebra (Ω*(M),ddR) of differential forms:
Procedure 1 (synthetic geometry).
For each n, consider the object ...

**5**

votes

**3**answers

482 views

### Derivations of C(X)? or Why Must Supermanifolds be Smooth?

What are the derivations of the algebra of continuous functions on a topological manifold?
A supermanifold is a locally ringed space (X,O) whose underlying space is a smooth manifold X, and whose ...