Proving that the tangent bundle of the sphere is projective but not free
122387
Is a stably free module always free?
124713
Projective space is not affine
108909
Is the unit sphere in $\Bbb R^4$ path connected?
70082
Show: Quotient space is homeomorphic to unit sphere
115347
Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage
21198
Proving that the general linear group is a differentiable manifold
68014
Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
154303
Degree $1$ map from torus to sphere
92033
Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
114640
Showing that an ideal is not a free $R-$module.
92504
Criteria of a trivial G bundle of a 3-manifold
129875
Fixed point theorem on spheres
61628
Does every smooth local frame of the tangent bundle correspond to a chart?
666
Prove that the upper half plane of Cartesian plane is not an affine variety
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
135059
Prove that the unit circle, $S^1:=\{(x,y)\in \mathbb{R}^2: x^2+y^2=1\}$, Is a one-dimensional manifold