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update README. Add small projects, which anyone could work on

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Floris van Doorn 2017-07-17 16:09:09 +01:00
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README.md
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Formalization project of the CMU HoTT group to formalize the Serre spectral sequence.
*Update July 16*: The construction of the Serre spectral sequence has been completed. The result is `serre_convergence` in `homotopy.serre`.
*Update July 16*: The construction of the Serre spectral sequence has been completed. The result is `serre_convergence` in `cohomology.serre`.
The main algebra part is in `algebra.spectral_sequence`.
This repository also contains the contents of the MRC group on formalizing homology in Lean.
@ -71,6 +71,14 @@ These projects are done
- Steenrod squares
- ...
#### To do (short-term easy projects)
- Compute cohomology groups of `K(ℤ, n)`
- Compute cohomology groups of `ΩSⁿ`
- Show that all fibration sequences between spheres are of the form `Sⁿ → S²ⁿ⁺¹ → Sⁿ⁺¹`.
- Compute fiber of `K(φ, n)` for group hom `φ` in general and if it's injective/surjective
- [Steve] Prove `Σ (X × Y) ≃* Σ X ∨ Σ Y ∨ Σ (X ∧ Y)`, where `Σ` is suspension. See `homotopy.susp_product`
#### In Progress
- [prespectra](http://ncatlab.org/nlab/show/spectrum+object) and [spectra](http://ncatlab.org/nlab/show/spectrum), indexed over an arbitrary type with a successor
+ think about equivariant spectra indexed by representations of `G`