New posts in Fundamental Groups

Compute fundamental group _visually_ by the polygonal representation of the space

Find finite path connected topological space with $π_1 (X, x_0 ) \cong \Bbb Z/2\Bbb Z$

How is going around the circle once in each direction homotopic to a point?

There is no 3-dimensional manifold with fundamental group isomorphic to direct sum of four copies of $\Bbb Z$

Is the Fundamental Groupoid a Bicategory?

Is every group homomorphism the induced homomorphism of a continuous function?

Fundamental group determined by connected components

Motivation for learning about fundamental groups and covering spaces

When van Kampen Fails

Looking for theorem of form: If [curvature hypotheses, etc] then every class in $\pi_1(M)$ is uniquely represented by a closed geodesic