dorsal/arxiv
View SchemaEffective generalized Seifert-Van Kampen: how to calculate $\Omega X$
| Authors | Carlos Simpson |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710011 |
| URL | https://arxiv.org/abs/q-alg/9710011 |
Abstract
Suppose $X$ is a 1-connected simplicial set with finitely many nondegenerate simplices. We give an effective algorithm to calculate a simplicial set with the $n$-type of the loop space $\Omega X$. Iterating gives an algorithm to calculate the $\pi_i(X)$, different from the algorithms already known due to E. Brown and Kan-Curtis. The method is an effective version of the generalized Seifert-Van Kampen theorem of alg-geom/9704006. This can be viewed as a Van Kampen statement concerning the loop space $\Omega X$ with its delooping structure. We use Segal's delooping machinery but at the end we speculate on extensions to other delooping machinery.
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"date_created": "2026-03-02T18:01:28.419000Z",
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"abstract": "Suppose $X$ is a 1-connected simplicial set with finitely many nondegenerate\nsimplices. We give an effective algorithm to calculate a simplicial set with\nthe $n$-type of the loop space $\\Omega X$. Iterating gives an algorithm to\ncalculate the $\\pi_i(X)$, different from the algorithms already known due to E.\nBrown and Kan-Curtis. The method is an effective version of the generalized\nSeifert-Van Kampen theorem of alg-geom/9704006. This can be viewed as a Van\nKampen statement concerning the loop space $\\Omega X$ with its delooping\nstructure. We use Segal\u0027s delooping machinery but at the end we speculate on\nextensions to other delooping machinery.",
"arxiv_id": "q-alg/9710011",
"authors": [
"Carlos Simpson"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Effective generalized Seifert-Van Kampen: how to calculate $\\Omega X$",
"url": "https://arxiv.org/abs/q-alg/9710011"
},
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