Talk:Serre spectral sequence

Sphere Bundle Fibration

This page should discuss examples of sphere fibrations and show how this gives a non-trivial spectral sequence with a torsion term. pg. 21-22 of http://math.stanford.edu/~galatius/282B15/spectral.pdf. An excellent example is $\mathcal{O}(k)\oplus \mathcal{O}(k) \to \mathbb{CP}^2$. Use the fact that the euler class is just the top chern class of the vector bundle, so in this case $e(E)=klc_{1}^{2}$ . — Preceding unsigned comment added by 50.246.213.170 (talk) 19:31, 12 August 2017 (UTC)[reply]

The above discussion, like the article's subsection concerning sphere bundles over K3 surfaces, is unhelpful and seriously misguided. The correct point to make here is that the Serre Spectral sequence of the sphere bundle of ANY oriented vector bundle just yields the GYSIN SEQUENCE, a nice, simple exact sequence in which the connecting homomorphisms are all just given by cupping with the Euler class of the relevant vector bundle. I strongly suggest that the relevant section of the article be replaced in its entirety! — Preceding unsigned comment added by 74.108.33.11 (talk) 18:39, 15 March 2020 (UTC)[reply]

Cohomology of Eilenberg-Maclane spaces

This page should discuss the computation of the rational cohomology for Eilenberg-Maclane spaces. A good source is https://www.ma.utexas.edu/users/a.debray/lecture_notes/u17_introduction_to_spectral_sequences.pdf — Preceding unsigned comment added by 50.246.213.170 (talk) 21:07, 24 November 2017 (UTC)[reply]

Lens Spaces

https://www.math.wisc.edu/~maxim/spseq.pdf — Preceding unsigned comment added by Wundzer (talk • contribs) 19:22, 9 February 2020 (UTC)[reply]