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fundamental group of a simplicial set?

asked 2024-01-11 16:45:50 +0200

anonymous user

Anonymous

I am working with simplicial sets in sagemath. I see a fundamental_group() method in the documentation, but it doesn't seem to work for my simplicial set:

from sage.topology.simplicial_set import *
a = AbstractSimplex(0, name='a')
b = AbstractSimplex(0, name='b')
e = AbstractSimplex(1, name='e')
f = AbstractSimplex(1, name='f')

S = SimplicialSet({e:(a,b), f:(b,a)})

S.homology() # this works
S.fundamental_group() # this doesn't work

(sorry not enough karma for a sagecell link)

The fundamental_group() method seems to work fine if I use the built-in example, like:

S = simplicial_sets.Sphere(1)

Is this method not supported on simplicial sets that are built "by hand"?

(My actual goal is to use a specific complicated example that I built by-hand, so I can't just use the built-in examples.

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answered 2024-01-11 18:32:05 +0200

Fundamental groups are only defined if you specify a base point. Given your setup:

S_based = S.set_base_point(a)
S_based.fundamental_group() # will now work

The documentation is here.

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Asked: 2024-01-11 16:45:50 +0200

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Last updated: Jan 11