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Computing the cohomology of Eilenberg Maclane spaces is a feasible but difficult problem in algebraic topology. The general answer is quite complicated (see the MO answer and the reference therein http://mathoverflow.net/a/24759/184https://mathoverflow.net/a/24759/184 )

However the cohomology of K(Z,2) is quite simple, it is just a polynomial algebra on a generator in degree two. I am wondering about the next easiest case.

What is the integral cohomology ring of K(Z,3)?

You can get quite far with spectral sequence calculations, but if this is worked out in detail somewhere, why reinvent the wheel?

Computing the cohomology of Eilenberg Maclane spaces is a feasible but difficult problem in algebraic topology. The general answer is quite complicated (see the MO answer and the reference therein http://mathoverflow.net/a/24759/184 )

However the cohomology of K(Z,2) is quite simple, it is just a polynomial algebra on a generator in degree two. I am wondering about the next easiest case.

What is the integral cohomology ring of K(Z,3)?

You can get quite far with spectral sequence calculations, but if this is worked out in detail somewhere, why reinvent the wheel?

Computing the cohomology of Eilenberg Maclane spaces is a feasible but difficult problem in algebraic topology. The general answer is quite complicated (see the MO answer and the reference therein https://mathoverflow.net/a/24759/184 )

However the cohomology of K(Z,2) is quite simple, it is just a polynomial algebra on a generator in degree two. I am wondering about the next easiest case.

What is the integral cohomology ring of K(Z,3)?

You can get quite far with spectral sequence calculations, but if this is worked out in detail somewhere, why reinvent the wheel?

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Chris Schommer-Pries
Chris Schommer-Pries
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Integral cohomology ring of K(Z,3)

Computing the cohomology of Eilenberg Maclane spaces is a feasible but difficult problem in algebraic topology. The general answer is quite complicated (see the MO answer and the reference therein http://mathoverflow.net/a/24759/184 )

However the cohomology of K(Z,2) is quite simple, it is just a polynomial algebra on a generator in degree two. I am wondering about the next easiest case.

What is the integral cohomology ring of K(Z,3)?

You can get quite far with spectral sequence calculations, but if this is worked out in detail somewhere, why reinvent the wheel?