Is there any domain $\Omega\subset\mathbb{R}^3$ with nontrivial homotopy group but with trivial first homology?
50587
Example of a domain in R^3, with trivial first homology but nontrivial fundamental group
91956
Intuition of the meaning of homology groups
86272
A topological space $X$ who can be $drawn$, whose fundamental group is $S_3$
4462
Homotopy invariance for cohomology
42412
Singular homology $S^{n}$ with rational coefficients
112607
Why is homology invariant under deformation retraction/homotopy equivalence?
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
82989
T4 and first countable topology that is non metrizable
91129
Can there be an onto homomorphism from a ring without unity to a ring with unity?
128118
Is the cofinite topology on a countable set first countable?
77563
Homeomorphism between spaces equipped with cofinite topologies
90010
Can we ascertain that there exists an epimorphism $G\rightarrow H$?
13764
Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
22150
The only 1-manifolds are $\mathbb R$ and $S^1$
92303
Homology of $S^1 \times (S^1 \vee S^1)$
145220
Homology Groups of $S^n$
95867
Subgroup of $C^*$ (nonzero complex) with finite index.