{
  "id": "cell-complexes-and-covering-spaces",
  "title": "Cell complexes, fundamental groups and covering spaces",
  "description": "Cell complexes, fundamental groups and covering spaces as used by the courses on group rings and classifying spaces: homotopy equivalences of cell complexes, trees, triangulations and simplicial approximation; fundamental groups of graphs and of complexes with attached cells, presentation complexes; universal covers with lifted cells and deck transformations, covers for normal subgroups, and cellular chains over the group ring with the Cayley complex.",
  "units": [
    {
      "id": "cell-complexes-and-homotopy-equivalences",
      "title": "Cell complexes and homotopy equivalences",
      "reader": "cell-complexes-and-homotopy-equivalences.html",
      "source": "src/cell-complexes-and-homotopy-equivalences.md",
      "source_sha256": "bff61f264af1abebd91ade6cd4577d2b75f9ecad8f1df415695bac718cc9ec0a",
      "status": "author_self_checked"
    },
    {
      "id": "fundamental-groups-of-graphs-and-two-complexes",
      "title": "Fundamental groups of graphs and two-complexes",
      "reader": "fundamental-groups-of-graphs-and-two-complexes.html",
      "source": "src/fundamental-groups-of-graphs-and-two-complexes.md",
      "source_sha256": "76acde0a90c9b9d966e350c8782d00a56394a5952421b5799c287b41e711da7a",
      "status": "author_self_checked"
    },
    {
      "id": "universal-covers-and-cellular-chains",
      "title": "Universal covers and cellular chains",
      "reader": "universal-covers-and-cellular-chains.html",
      "source": "src/universal-covers-and-cellular-chains.md",
      "source_sha256": "3801095c245cbf16ffb306f06c76c0e7a59f9d58fdb9dfdb9c5f31c028f2c42a",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "core course Algebraic Topology (D60), edition with Roberts's lectures and Fomberg's components: Lecture 4 Definition 4.4; Lecture 5 Theorem 5.1 and Corollary 5.3; Lecture 6 Definition 6.2; Lecture 7 Proposition 7.1, Definition 7.1, Lemma 7.1 and Corollary 7.1; Lecture 9 Corollaries 9.1 and 9.4; Lecture 10 Theorem 10.1 and Corollary 10.1; Lecture 12 Example 12.2 and Corollary 12.1; Lecture 16 Definition 16.1, Propositions 16.1 and 16.2 and Corollary 16.1; Lecture 17 Lemma 17.1; Lecture 18 Lemma 18.2 and Proposition 18.2; Fomberg component 7 (lemma on skeleta, cellular homology theorem (14.1)-(14.2), incidence formula with (15.3)); Fomberg Theorem 1.13 and Corollary 1.14",
    "programme course Characteristic classes (DG-CHAR): lesson Grassmannians and classifying maps (DG-CHAR-03), Section 7 (Lemma 7.1, product of a quotient map with the interval, Lemma 7.2) and Theorem 8.3 with the paragraph after its proof; lesson Frame fields and primary obstructions (DG-CHAR-08B), Lemma A.1 and its proof, homotopy extension in Section E, Lemma E.1",
    "programme course Van Kampen diagrams (van-kampen-diagrams): lesson Words, free groups and Cayley graphs (Lemmas 1.1, 1.2, 3.1, 3.3, Definition 4.1, Lemma 4.2, Exercise 5.2)"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}