Effective generalized SeifertVan Kampen: how to calculate $\Omega X$
Abstract
Suppose $X$ is a 1connected 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 KanCurtis. The method is an effective version of the generalized SeifertVan Kampen theorem of alggeom/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.
 Publication:

eprint arXiv:qalg/9710011
 Pub Date:
 October 1997
 DOI:
 10.48550/arXiv.qalg/9710011
 arXiv:
 arXiv:qalg/9710011
 Bibcode:
 1997q.alg....10011S
 Keywords:

 Quantum Algebra and Topology;
 Mathematics  Quantum Algebra
 EPrint:
 Fixes a notational error in the example: \wedge now replaced by \vee. 40 pages