Reduced L_q,p-Cohomology of Some Twisted Products

2015/05/05 by Vladimir Gol'dshtein, Gol'dshtein, Vladimir, Yaroslav Kopylov +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.1505.00913

15 pages

arxiv created 2015/09/27 · arxiv updated 2015/09/29

Abstract

Vanishing results for reduced L_p,q-cohomology are established in the case of twisted products, which are a~generalization of warped products. Only the case q ≤ p is considered. This is an extension of some results by Gol'dshtein, Kuz'minov and Shvedov about the L_p-cohomology of warped cylinders. One of the main observations is the vanishing of the "middle-dimensional" cohomology for a large class of manifolds. This means that the L₂-Betty numbers are zero in the "middle dimension".

Related

• L_p,q-Cohomology of Warped Cylinders
• The Sobolev--Poincar 'e Inequality and the L_q,p-Cohomology of\n Twisted Cylinders
• Distortion of Mappings and L_q,p-Cohomology
• On the L_q,p-cohomology of Riemannian Manifolds with Negative Curvature
• A vanishing theorem in twisted de Rham cohomology