Nerves, fibers and homotopy groups
2003 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 102, no 1, 88-93 p.Article in journal (Refereed) Published
Two theorems are proved. One concerns coverings of a simplicial complex Delta by subcomplexes. It is shown that if every t-wise intersection of these subcomplexes is (k - t + 1)-connected, then for jless than or equal tok there are isomorphisms pi(j)(Delta) congruent to pi(j)(N) of homotopy groups of Delta and of the nerve X of the covering. The other concerns poset maps f : P --> Q. It is shown that if all fibers f(-1)(Q(less than or equal toq)) are k-connected, then f induces isomorphisms of homotopy groups pi(j)(P) congruent to pi(j)(Q), for all jless than or equal tok.
Place, publisher, year, edition, pages
2003. Vol. 102, no 1, 88-93 p.
IdentifiersURN: urn:nbn:se:kth:diva-22446DOI: 10.1016/s0097-3165(03)00015-3ISI: 000182429700006OAI: oai:DiVA.org:kth-22446DiVA: diva2:341144
QC 201005252010-08-102010-08-10Bibliographically approved