If M is a non-orientable closed connected 3 manifold prove H1(M) is an infinite group.
94708
Non-orientable 3-manifold has infinite fundamental group
78624
CW complexes and manifolds
102485
Showing that a topological space is ${\rm T}_1$
157742
Prove that $U(n)$ is a manifold
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
154398
Show that H is a subgroup of G
142698
Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
22150
The only 1-manifolds are $\mathbb R$ and $S^1$
27661
The closed graph theorem in topology
153921
Infinite nilpotent group, any normal subgroup intersects the center nontrivially
90764
Prove that the fundamental group of the circle is non-trivial if the fundamental group of a space $X$ is non-trivial
50587
Example of a domain in R^3, with trivial first homology but nontrivial fundamental group
72190
Topological proof on discrete topology where $X$ is infinite
129943
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
97637
Showing that isotropy groups are submanifolds
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
135059
Prove that the unit circle, $S^1:=\{(x,y)\in \mathbb{R}^2: x^2+y^2=1\}$, Is a one-dimensional manifold