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Nerves, fibers and homotopy groups
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-7497-2764
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
Abstract [en]

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.
Identifiers
URN: urn:nbn:se:kth:diva-22446DOI: 10.1016/s0097-3165(03)00015-3ISI: 000182429700006OAI: oai:DiVA.org:kth-22446DiVA: diva2:341144
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Björner, Anders

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