Point Set Topology

Munkres

Leinster - General topology

Homeomorphism

https://en.wikipedia.org/wiki/Homeomorphism https://en.wikipedia.org/wiki/Simplicial_complex_recognition_problem

https://en.wikipedia.org/wiki/Triangulation_(topology)

Brouwer fixed point https://en.wikipedia.org/wiki/Sperner%27s_lemma

jordan curve theorem

covering spaces

fundamental polyhedron - polyhedra schema. Those diagram with glued edges. The edges are generators

Algebraic Topology

algerbaic topology hatcher

Peter May - Algebraic Topology a concise course

Complexes

simplicial-complex - maybe the kind of obvious one. Triangulate your space.
delta-complex https://en.wikipedia.org/wiki/Delta_set delta set, semisimplicial set
CW-complex - Bread and butter
simplicial set https://en.wikipedia.org/wiki/Delta_set
Kan complex

# toy around with hap definitions

class CW():

#triangle
points = [None,None,None]
edges = [(0,1), (1,2), (2,0)]
faces = [(0,1,2)] # indices refer to previous

# square
points = [None,None,None,None]
edges = [(0,1), (1,2), (2,3), (3,0)]
faces = [(0,1,2,3)] # indices refer to previous

Discrete finite represntation of CW uses loops over previous layers. The “disk” is a polygon. This is nice compared to simplicial because there is a nicer notion of “simplyfing” a space by removing redundant subdivision.

Regular vs non regular

Homotopy

Deformation Retract- $f_t : X -> X$ s.t. $f_0 = id$ and f_1 = A and f_t(A) = A for all t. It leaves A alone for all t. https://en.wikipedia.org/wiki/Retraction_(topology). Retraction is projection to subspace that preserves all points in subspace.

https://en.wikipedia.org/wiki/Inclusion_map

Homology

Morse Theory

Computational Topology

https://en.wikipedia.org/wiki/Computational_topology https://www.computop.org/ lots of cool programs

computatonal toploggy edelsbrunner harer notes

haskell rewrite of kenzo

HAP GAP https://docs.gap-system.org/pkg/hap/www/index.html graham ellis. Book https://www.youtube.com/watch?v=UMpTTuRdMA0&ab_channel=InstitutFourier

http://snappy.computop.org/ snappea for 3 manifolds. python bindings http://snappy.computop.org/verify_canon.html canonical retriangulation / cell decoomposition geometrization theorem dehn-filling There’s like a canonical geometrical surface? And then metrical things like volume are cannical?

uniformizaton

http://chomp.rutgers.edu/ chomp computational homology

exact reals? hott?

toploogical data anaysis persistent topology

seifert

computational group theory MAF https://maffsa.sourceforge.net/manpages/MAF.html KBMAG automata to describe the multiplication operation