Algebraic Topology Crossword

Edit Answers
12345678910111213141516171819202122232425262728293031323334353637383940414243444546
Across
  1. 1. The fundamental group of a torus
  2. 5. A theorem used to deduce that every map D^2 -> D^2 has a fixed point
  3. 9. This colimit of two morphisms with a common domain always exists in Top
  4. 10. The number of points on the true/false section of the Math 592 Winter 2023 midterm exam
  5. 12. The _____ characteristic of any convex polyhedron is 2
  6. 14. A regular covering space corresponds with a _____ subgroup
  7. 16. Common name for the category of spaces and homotopy classes of maps
  8. 17. The torus has 1, and S^2 has 0
  9. 18. Each disjoint open set in a covering space that maps homeomorphically onto a neighborhood
  10. 22. The group of words on a set of generators
  11. 23. H_1 as it relates to π_1
  12. 24. A theorem used to deduce that H_n(X) = π_n(X) for n ≥ 2 if X is (n-1)-connected
  13. 26. Abbreviation for a necessary condition for a space to have a universal cover
  14. 28. Homology of a CW complex
  15. 29. This unique path always exists from a given covering space
  16. 30. A non-orientable surface homotopy equivalent to S^1
  17. 31. The Math 592 instructor for Winter 2023
  18. 33. A 1-dimensional CW complex
  19. 34. A property of the universal cover of S^1 v S^1
  20. 38. A continuous map XxI -> Y
  21. 39. ker(d)/im(d) in a cochain complex
  22. 40. A theorem used to deduce that f : X -> Y is a homotopy equivalence if π_n(X) = π_n(Y) for all a
  23. 44. Common name for the category of groups
  24. 45. A product used on cochain maps
  25. 46. A certain collection of objects and morphisms
Down
  1. 2. The student who submitted this crossword as an assignment
  2. 3. A theorem used to compute the homology of a Cartesian product
  3. 4. A continuous map f : I -> X
  4. 6. The group of homotopy classes of loops with the natural product operation
  5. 7. This is -1 for a reflection of S^n
  6. 8. The fundamental group of a simply-connected space
  7. 11. The 0th _____ homology group is 0
  8. 13. ker(d)/im(d) in a chain complex
  9. 15. A space whose fundamental group is <a,b | abab^{-1}>
  10. 18. Van Kampen's lesser-known partner
  11. 19. A long exact sequence used to compute the homology of an open cover
  12. 20. A theorem used to compute the fundamental group of an open cover
  13. 21. Another name for a normal covering space
  14. 22. π_1 and H_n are examples of this
  15. 25. No such map from D^2 to S^1 exists
  16. 26. The universal cover of RP^n
  17. 27. The space CX = (XxI)/(Xx{0}) for a space X
  18. 32. Homology of a Δ-complex
  19. 35. The universal cover of a torus
  20. 36. An open disk in a CW complex
  21. 37. Used to compute relative homology
  22. 40. A sum that joins two spaces at a point
  23. 41. Short _____ sequence of homomorphisms
  24. 42. The topology on a CW complex
  25. 43. The set of lines through the origin in R^(n+1)