# What does $\Omega^\bullet(M)$ mean?

What does $\Omega^\bullet(M)$ mean?

I know that $\Omega^k(M)$ is the set of all differential k-forms.

$\Omega^\bullet(M) = \bigoplus_{k=0}^{\dim M} \Omega^k(M)$ is the space of all differential forms, which is $\mathbb Z$ graded by degree.
thanks for your quick answer! I'm reading this: math.ist.utl.pt/~acannas/Books/lsg.pdf (page 36, PDF page 44). There we have both $\Omega^\bullet$ and $\Omega^\*$. So what is the difference? – user1135859 Apr 24 '13 at 13:01
There really is no difference. $\bullet$ and $*$ are often used interchangeably when denoting $\mathbb Z$-graded objects. $\bullet$ may be the better notation though since $*$ is also used for dual. – Eric O. Korman Apr 24 '13 at 14:43