Combinatorial 8-Manifolds having Cohomology of the Quaternionic Projective Plane and Their Nonembeddings

From NZJM

Jump to: navigation, search

New Zealand Journal of Mathematics

Vol. 44, (2014), Pages 15-20


Satya Deo

Harish-Chandra Research Institute,

Chhatnag Road, Jhusi,

Allahabad 211 019, India.


mailto:sdeo@mri.ernet.in mailto:vcsdeo@yahoo.com






Abstract In this paper we prove, using Z2index theory, that none of the three combinatorial 8-manifolds on 15 vertices constructed by Brehm and K├╝hnel, each of which is a cohomology quaternionic projective plane, can be combinatorially embedded in the Euclidean space E12, though they have tight polyhedral embeddings in E14. This extends a similar result, including the method of proof, already known for the nonembeddings of real and complex projective planes.

Keywords Factorization; Combinatorial manifolds, cohomology quaternionic projective plane, BK complexes, G-index of a G-space.

Classification (MSC2000) Primary 57Q15, 55N25, Secondary: 54G15

Full text

Full paper

Personal tools