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feat(hott): update book.md and homotopy.md to reflect additions

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Ulrik Buchholtz 2016-03-06 20:03:27 -05:00 committed by Leonardo de Moura
parent f11169b8f2
commit 7e8ba1440f
2 changed files with 22 additions and 11 deletions
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14
hott/book.md
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@ -22,7 +22,7 @@ The rows indicate the chapters, the columns the sections.
| Ch 5 | - | . | ½ | - | - | . | . | ½ | | | | | | | |
| Ch 6 | . | + | + | + | + | ½ | ½ | + | ¾ | ¼ | ¾ | + | . | | |
| Ch 7 | + | + | + | - | ¾ | - | - | | | | | | | | |
| Ch 8 | + | + | + | - | ¼ | ¼ | - | - | - | - | | | | | |
| Ch 8 | + | + | + | - | ¾ | ¼ | - | - | - | - | | | | | |
| Ch 9 | ¾ | + | + | ½ | ¾ | ½ | - | - | - | | | | | | |
| Ch 10 | - | - | - | - | - | | | | | | | | | | |
| Ch 11 | - | - | - | - | - | - | | | | | | | | | |
@ -139,14 +139,14 @@ Chapter 7: Homotopy n-types
Chapter 8: Homotopy theory
---------
Unless otherwise noted, the files are in the folder [homotopy](homotopy/homotopy.md)
Every file is in the folder [homotopy](homotopy/homotopy.md)
- 8.1 (π_1(S^1)): [homotopy.circle](homotopy/circle.hlean) (only the encode-decode proof)
- 8.2 (Connectedness of suspensions): [homotopy.connectedness](homotopy/connectedness.hlean) (different proof of Theorem 8.2.1)
- 8.3 (πk≤n of an n-connected space and π_{k<n}(S^n)): [homotopy.homotopy_group](homotopy/homotopy_group.hlean)
- 8.1 (π_1(S^1)): [circle](homotopy/circle.hlean) (only the encode-decode proof)
- 8.2 (Connectedness of suspensions): [susp](homotopy/susp.hlean) (different proof of Theorem 8.2.1)
- 8.3 (πk≤n of an n-connected space and π_{k<n}(S^n)): [homotopy_group](homotopy/homotopy_group.hlean)
- 8.4 (Fiber sequences and the long exact sequence): not formalized
- 8.5 (The Hopf fibration): [homotopy.circle](homotopy/circle.hlean) (H-space structure on the circle, Lemma 8.5.8), [homotopy.join](homotopy/join.hlean) (join is associative, Lemma 8.5.9), the rest is not formalized
- 8.6 (The Freudenthal suspension theorem): [homotopy.connectedness](homotopy/connectedness.hlean) (Lemma 8.6.1), [homotopy.wedge](homotopy/wedge.hlean) (Wedge connectivity, Lemma 8.6.2), the rest is not formalized
- 8.5 (The Hopf fibration): [circle](homotopy/circle.hlean) (multiplication on the circle, Lemma 8.5.8), [join](homotopy/join.hlean) (join is associative, Lemma 8.5.9), [hopf](homotopy/hopf.hlean) (The Hopf construction, Lemmas 8.5.5 and 8.5.7), [complex_hopf](homotopy/complex_hopf.hlean) (the H-space structure on the circle and the complex Hopf fibration)
- 8.6 (The Freudenthal suspension theorem): [connectedness](homotopy/connectedness.hlean) (Lemma 8.6.1), [wedge](homotopy/wedge.hlean) (Wedge connectivity, Lemma 8.6.2), the rest is not formalized
- 8.7 (The van Kampen theorem): not formalized
- 8.8 (Whitehead’s theorem and Whitehead’s principle): not formalized
- 8.9 (A general statement of the encode-decode method): not formalized

17
hott/homotopy/homotopy.md
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@ -5,15 +5,26 @@ Development of Homotopy Theory, including basic hits (higher inductive
types; see also [hit](../hit/hit.md)). The following files are in this
folder (sorted such that files only import previous files).
* [connectedness](connectedness.hlean) (n-Connectedness of types and functions)
* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)
* [susp](susp.hlean) (Suspensions, defined using pushouts)
* [red_susp](red_susp.hlean) (Reduced suspensions)
* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)
* [circle](circle.hlean) (defined as sphere 1)
* [torus](torus.hlean) (defined as a two-quotient)
* [interval](interval.hlean) (defined as the suspension of unit)
* [cellcomplex](cellcomplex.hlean) (general cell complexes)
* [connectedness](connectedness.hlean)
* [cofiber](cofiber.hlean)
* [wedge](wedge.hlean)
* [smash](smash.hlean)
* [homotopy_group](homotopy_group.hlean) (theorems about homotopy groups. The definition and basic facts about homotopy groups is in [algebra/homotopy_group](../algebra/homotopy_group.hlean)).
* [join](join.hlean)
* [hopf](hopf.hlean) (the Hopf construction and delooping of coherent connected H-spaces)
* [complex_hopf](complex_hopf.hlean) (the complex Hopf fibration)
* [imaginaroid](imaginaroid.hlean) (imaginaroids as a variant of the Cayley-Dickson construction)
* [quaternionic_hopf](quaternionic_hopf.hlean) (the quaternionic Hopf fibration)
The following files depend on
[hit.two_quotient](../hit/two_quotient.hlean) which on turn depends on
[circle](circle.hlean).
* [red_susp](red_susp.hlean) (Reduced suspensions)
* [torus](torus.hlean) (defined as a two-quotient)