Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

So the equivalence class [itex]X/\sim[/itex] is the set of all equivalences classes [itex][x][/itex]. I was wondering if there was a way of writing it in terms of the usual quotient operation:

[tex]G/N=\{gN\ |\ g\in G\}?[/tex]

From what I've read, it would be something like [itex]X/\sim = X/[e][/itex]. But, since I'm looking at the de Rham cohomology group [itex]H^k = \{ closed\ k\ forms\}/\sim[/itex] so

[tex]H^k = \{ closed\ k\ forms\}/[0] = \{ \omega [0]\ |\ \omega\ is\ a\ closed\ form\}[/tex]

doesn't work, as the the operation [itex]\omega [0][/itex] doesn't seem to make sense.

It's also defined [itex]H^k = Z^k/B^k[/itex] if you're familiar with that notation.

Any thoughts?

Cheers

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quotient set of equivalence class in de Rham cohomology

**Physics Forums | Science Articles, Homework Help, Discussion**