Postnikov tower

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Tags
- #subjects/homotopy
Refs:
- Lecture Notes: <https://webspace.science.uu.nl/~caval101/homepage/Geometry_and_Topology_2015_files/Groth - lecture notes on homotopy theory.pdf>
  - Includes Postnikov and Whitehead towers
- https://www.math.purdue.edu/~zhang24/towers.pdf
Links:
- #todo/create-links

Notes

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Links to this page

unresolved links output

k-invariant in -Atiyah Hirzebruch spectral sequence, -Postnikov tower
spin

Explanation of string structure by vanishing of characteristic classes, using the Whitehead tower. Essentially it all depends on \(\pi_* {\operatorname{O}}_n\):
basic tools in homotopy of spaces

Postnikov tower
Griffiths and Morgan Reading Notes

This DGA of smooth forms is actually enough to calculate all of the AT invariants, and can be used to build the Postnikov tower of \(M\) (\(\otimes{\mathbb{R}}\))
CW complex

Postnikov tower

For Postnikov towers:
2021-10-05 quick_notes

Postnikov invariants: File:attachments/2021-10-05_20-41-56.png
2021-04-25_classifying_hotop_blog_ideas

The moral of the story here is that we can generalize a product of spaces \(A \times B \times C \times \cdots\) as a “twisted product” \(A \rtimes_{\varphi_1} B \rtimes_{\varphi_1} C \rtimes_{\varphi_1} \cdots\) by constructing an interlocking series of fibrations. Luckily for us, our next step towards solving our original problem will involve the construction of Postnikov tower, which explicitly encode how this interlocking works.