mathematicskit.topology
=======================


.. include:: /_generated/nav/topology.rst

Simplicial complexes with signed boundary matrices, standard
triangulations (spheres, torus, Klein bottle, Möbius strip, projective
plane), barycentric subdivision and products; the Smith normal form,
Betti numbers over :math:`\mathbb{Q}` or :math:`\mathbb{Z}/p`, integer
homology with torsion, and the Mayer-Vietoris sequence; the fundamental
group; orientability, the classification of surfaces and Banchoff's
critical points; Sperner's lemma, Brouwer fixed points, vector-field
indices and Lefschetz numbers; Gauss's linking number and Hopf's
turning number; and Vietoris-Rips and Čech complexes, persistent
homology, the bottleneck distance and Mapper.

.. automodule:: mathematicskit.topology
   :members:
   :undoc-members: