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I need a book or more books with a lot (plenty) of exercises , maybe solutions also that could cover entirely my course that is called geometry 2 ,but for sure it will have other denominations . My course is divided in 3 parts and these are topics:

first part general topology

  1. topological spaces: construction and examples of subspaces , product , quotients
  2. topological propriety: separation, numerability , compactness, ,Arc connectedness, connected spaces
  3. topological variety and classificatin of topological compact surfaces

second part :introduction to algebraic topology

  1. homotopy of paths and of continuous application .
  2. foundamental group and omotopic invariance.
  3. van Kampen 's theorem and application .
  4. Covering space and relation with foundamental group
  5. construction of universal cover

third part :introduction to differential geometry of curves and surfices

  1. differential curves in euclidian spaces

  2. tangent line, curvature, torsion and rigidity theorem.

  3. differential surfeces.

  4. tangent plane and first foundamental form .

  5. second foundamental form and curvature invariant .

  6. gaussian Curvature and egregium theorem .

thanks for reading and for suggestions

Cristin
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    Your uni surely has provided resources, since the course is so clearly laid out, no? It might help to explain what do you want from the site that the uni isn’t giving you – FShrike Feb 04 '22 at 09:03
  • @FShrikes In my uni professor gives his note and his own exercises, but i'd like to study on a book with exercises and solution possibly – Cristin Feb 04 '22 at 09:13
  • but i'd like to study on a book with exercises and solution possibly -- Why not just go to your university library and browse the shelves for books that appear suitable, since you know much more than we do about what you want regarding topics and mathematical maturity level and detail. For example, see the first two paragraphs of this answer (not for the topic itself, but the process of locating books). If there is a reason why this obvious process is not applicable in your case, then you should indicate your limitations in your question. – Dave L. Renfro Feb 04 '22 at 10:41

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