Rational analogs of projective planes
Geometric Topology
2016-01-20 v3 Algebraic Topology
Abstract
In this paper, we study the existence of high-dimensional, closed, smooth manifolds whose rational homotopy type resembles that of a projective plane. Applying rational surgery, the problem can be reduced to finding possible Pontryagin numbers satisfying the Hirzebruch signature formula and a set of congruence relations, which turns out to be equivalent to finding solutions to a system of Diophantine equations.
Cite
@article{arxiv.1010.3274,
title = {Rational analogs of projective planes},
author = {Zhixu Su},
journal= {arXiv preprint arXiv:1010.3274},
year = {2016}
}
Comments
Accepted for publication by Algebraic & Geometric Topology. Certain computational error corrected in Theorem 3.7