Combinatorial 8-Manifolds having Cohomology of the Quaternionic Projective Plane and Their Nonembeddings
Abstract
In this paper we prove, that none of the three combinatorial 8- manifolds on 15 vertices constructed by Brehm and Kuhnel, each of which is a cohomology quaternionic projective plane, can be combinatorially embedded in the Euclidean 12-space, though they have tight polyhedral embeddings in Euclidean 14-space. This extends a similar method already known for the nonembeddings of real and complex projective planes.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2013
- DOI:
- 10.48550/arXiv.1305.1165
- arXiv:
- arXiv:1305.1165
- Bibcode:
- 2013arXiv1305.1165D
- Keywords:
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- Mathematics - Algebraic Topology;
- 54G15;
- 55Q15;
- 57Q15
- E-Print:
- 8 pages