# The Groove of Math

## Filling the Details #5: Two words about the Atiyah-Hirzebruch Spectral Sequence

It’s finally time we shed some light on the technicalities behind this powerful tool. It took me some time digesting all these materials and I have to thank all the people who helped me understanding these passages. We will identify the differentials of the AHSS for spin-bordism (since it’s the one I need for my thesis), but the method we are going to use can be generalised to any AHSS, provided we have enough informations about the cohomology group of the spectra involved.

## Notes of a Seminar in Group Cohomology

I decided to share the notes I prepared for a Seminar I gave about Group Cohomology. To be more precise, I spoke about Finiteness Conditions and I studied a particular subgroup  of $SL_n(Z)$.

There might be some errors here and there, please read with cautions and let me know if you find something unclear!

pedrotti-riccardo-cohomology-of-groups

## Filling the Details #4: Maps of Eilenberg MacLane Spectra induces stable cohomology operations

First of all, sorry for not having written lately. I’ve just done the GRE and GRE math examinations, together with the TOEFL. I really hope the result will be good, since I’m going to apply in the USA!

Ok, back to Math 🙂  As the title suggests, I want to write something about this known result, since I needed it for understanding why the first non-vanishing differential in the Atiyah-Hirzebruch Spectral Sequence is a stable operation. What I’m going to show is not the nicest way to prove it, but still I think it’s worth to take a look at a more “concrete” proof