MrMineev

Poincaré Duality

Rewriting the proof of \(H_C^k(M;R) \cong H_{n-k}(M;R)\) so it sticks better in memory.

Some Applications of Casey

The circumcircle tangency criterion, a Feuerbach exercise, and two problems.

Taming the Yoneda Lemma

I have been struggling to properly understand the Yoneda lemma for a while

Homology of the Suspension

Reduced homology of the suspension \(\tilde{H}_n(SX) \cong \tilde{H}_{n-1}(X)\) and of \(k\) cones glued over a space.

Euler Characteristic

The Euler characteristic of a CW complex via the ranks of its homology groups.