Is there any difference between the free homotopy classes and homology classes of oriented loops in a closed oriented surface
140612
Two homologous but not homotopic loops on a closed surface of genus greater than one
30678
Direct proof that the wedge product preserves integral cohomology classes?
2871
Spaces with equal homotopy groups but different homology groups?
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
135126
Proving that the quotient manifold is orientable if and only if the group action is orientation-preserving
144072
Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
60008
Can we always view loops as maps from $S^1\to X$?
123656
Covering map between orientable compact connected surfaces without boundary with genus $g$
36676
Homotopy Visualization
39010
Metrization of the cofinite topology
23156
Homotopy equivalence from torus minus a point to a figure-eight.
149029
3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
124829
Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell
122410
Can one build a homology theory using submanifolds and their boundaries?
112607
Why is homology invariant under deformation retraction/homotopy equivalence?
24191
Computing the cohomology group of CW-Complex
76563
Category Theory usage in Algebraic Topology