@LeakyNun that's a finite-dimensional vector space...

@LeakyNun you send $\Lambda^k T^*_x M$ to $x$

I hope it's ok that I've mentioned this room in MathOverflow chatroom: chat.stackexchange.com/transcript/message/48388731#48388731

It was in connection with this question on their meta: Migrated to MSE, did not get enough attention. What to do? Perhaps the interests of the users who visit this room are not that far away from the questions mentioned in that post.

@MartinSleziak It's no problem, but this room should functionally be considered as a private room that everyone can view. The intent is to have a discussion place for a relatively small and close-knit group of people.

I agree that the original intent in the creation of this room was precisely that

But thanks for bringing our attention to those questions. If someone here is interested they'll look into those questions closely

@MikeMiller Well, I understand this from the fact that it's a gallery room. (But perhaps the next time I should ask here first.)

After all, it's up to you who you grant the access to the room..... Maybe I've just lost mine. :-)

In any case, I have also mentioned Geometry & Topology room - if that one is preferable in this specific situation. (However, that room seems to be empty for some time.)

@MartinSleziak Haha, you're ok. I just think we very very rarely grant new write access.

Just for convenience of people who want to take a look, I'll include the full titles and links of the questions referenced in the meta.MO question: Chern class cohomology coefficients complex/real/integral? and Chern class of a principal $G$ bundle for a compact Lie group $G$.

So that people who are willing to look at them do not have to go to the meta.MO first and get the links from there.