Please use this identifier to cite or link to this item:
Title: Nine-fields on manifolds
Authors: Ng, T.-B. 
Keywords: fourth-order cohomology operations
Steenrod algebra
Issue Date: 6-May-1991
Citation: Ng, T.-B. (1991-05-06). Nine-fields on manifolds. Topology and its Applications 39 (2) : 167-187. ScholarBank@NUS Repository.
Abstract: E. Thomas in 1969 in a survey paper "Vector Fields on Manifolds" (loc. cit.) made several conjectures about the span of manifolds. We solve Problem 5 of that paper, namely, that when n is congruent to 31 mod 32 and Mn is 7-connected, then Mn admits a tangent 9-field if, and only if, the mod 2 semi-Kervaire characteristic X2(M) vanishes. Indeed we obtain the same conclusion by requiring Mn to be only 7-connected mod 2 instead of 7-connected. We obtain necessary and sufficient conditions for an n-plane bundle ξ over Mn whose dimension n is congruent to 7 mod 8 with n > 15 to have span≥9. The results are applied to the tangent bundle of Mn and we prove one of Thomas's conjectures concerning the existence of 9-fields on such an n-dimensional manifold Mn. The method of proof consists in realizing the obstructions to the existence of 9 linearly independent sections to ξ via secondary, tertiary and fourth-order cohomology operations on the Thom class of ξ and the evaluation of these operations on the Thom class of the tangent bundle of Mn. We also prove that when n is congruent to 23 mod 32, span Mn≥8 implies span Mn≥9. © 1991.
Source Title: Topology and its Applications
ISSN: 01668641
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

checked on Aug 31, 2018

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.