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
- topological spaces: construction and examples of subspaces , product , quotients
- topological propriety: separation, numerability , compactness, ,Arc connectedness, connected spaces
- topological variety and classificatin of topological compact surfaces
second part :introduction to algebraic topology
- homotopy of paths and of continuous application .
- foundamental group and omotopic invariance.
- van Kampen 's theorem and application .
- Covering space and relation with foundamental group
- construction of universal cover
third part :introduction to differential geometry of curves and surfices
differential curves in euclidian spaces
tangent line, curvature, torsion and rigidity theorem.
differential surfeces.
tangent plane and first foundamental form .
second foundamental form and curvature invariant .
gaussian Curvature and egregium theorem .
thanks for reading and for suggestions