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Effective generalized Seifert-Van Kampen: how to calculate $ΩX$

Carlos Simpson
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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 $ΩX$. Iterating gives an algorithm to calculate the $π_i(X)$, 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 $ΩX$ 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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BibTeXRIS

Carlos Simpson. 1997-10-19. Effective generalized Seifert-Van Kampen: how to calculate $ΩX$. https://arxiv.org/abs/q-alg/9710011

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