2012/11/30 by Diarmuid Crowley, Johannes Nordström · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Connected sum #Geometric and Algebraic Topology #Holonomy #Homotopy #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Modulo #Simply connected space #Torsion (gastropod) #math.DG #math.GT #msc:53C10 #msc:53C25 #msc:53C27 #msc:57R15 #msc:57R50 #msc:57R90
paper · pdf · doi:10.2140/gt.2015.19.2949
published as Geom. Topol. 19 (2015) 2949-2992 · 26 pages, 1 figure. v3: Defined further invariant, strengthened classification results, changed title
arxiv created 2014/09/11 · openalex publication_date 2015/10/20 · arxiv updated 2015/10/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
We define a [math] –valued homotopy invariant [math] of a [math] –structure [math] on the tangent bundle of a closed [math] –manifold in terms of the signature and Euler characteristic of a coboundary with a [math] –structure. For manifolds of holonomy [math] obtained by the twisted connected sum construction, the associated torsion-free [math] –structure always has [math] . Some holonomy [math] examples constructed by Joyce by desingularising orbifolds have odd [math] . ¶ We define a further homotopy invariant [math] such that if [math] is [math] –connected then the pair [math] determines a [math] –structure up to homotopy and diffeomorphism. The class of a [math] –structure is determined by [math] on its own when the greatest divisor of [math] modulo torsion divides 224; this sufficient condition holds for many twisted connected sum [math] –manifolds. ¶ We also prove that the parametric [math] –principle holds for coclosed [math] –structures.