New posts in compact-manifolds

Geometric intuition for torsion in $H_{2}$ of non-orientable $3$-manifold

general-topology algebraic-topology visualization compact-manifolds

Euler characteristic of a manifold is odd

algebraic-topology homology-cohomology manifolds-with-boundary compact-manifolds

Finitely generated singular homology

algebraic-topology manifolds homology-cohomology compact-manifolds

Hairy Ball Theorem: homotopy from the identity to the antipodal map

algebraic-topology differential-topology compact-manifolds

Could exists a vector field on $\mathbb{S}^{2}$ with exactly $n$ zeroes?

differential-geometry smooth-manifolds vector-fields spheres compact-manifolds

Norm Inequality on a Compact Riemannian Manifold

partial-differential-equations manifolds riemannian-geometry compact-manifolds

Why spheres are not symplectic manifolds?

differential-geometry manifolds symplectic-geometry spheres compact-manifolds

Proof that a compact surface has a tangent plane orthogonal to position

differential-topology vector-analysis compact-manifolds

If the connected sum of a manifold $M$ with itself gives back $M$, does it imply $M$ is a sphere?

algebraic-topology compact-manifolds

Does there exist a compact submanifold of $\mathbb{R}^3$ whose fundamental group is $\mathbb{Z}^3$?

algebraic-topology homotopy-theory fundamental-groups submanifold compact-manifolds

Understanding Takens' Embedding theorem

differential-geometry differential-topology smooth-manifolds chaos-theory compact-manifolds

A non orientable closed surface cannot be embedded into $\mathbb{R}^3$

differential-geometry manifolds differential-topology surfaces compact-manifolds

Examples of manifolds that are not boundaries

algebraic-topology compact-manifolds cobordism