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- spectral sequence
- Exact Couples
- Atiyah Hirzebruch spectral sequence
- Gysin sequence
- spectral sequence of a double complex
- examples of cohomology rings
examples of spectral sequences
Evenly supported complexes
Loop spaces of spheres
#examples/explicit-computations
Computing
\begin{align*}
H_* {\Omega}S^n = \left\langle{ x_{n-1}, x_{2(n-1)}, x_{3(n-1)}, \cdots}\right\rangle
\end{align*}
Multiplicative structure
Appearance of a divided power algebra.
Computing for Eilenberg-MacLane spaces
#examples/explicit-computations
Computing
\begin{align*}
H_*( K({\mathbf{Z}}, 2); {\mathbf{Z}}) = {\mathbf{Z}} { \left[ \scriptstyle {x} \right] } , \qquad {\left\lvert {x} \right\rvert} = 2
\end{align*}
Group cohomology
Used to study Serre classes:
p torsion in \(\pi_{2p}S^3\)
An example of working one prime at a time:
