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.
Citation
Zhixu Su. "Rational analogs of projective planes." Algebr. Geom. Topol. 14 (1) 421 - 438, 2014. https://doi.org/10.2140/agt.2014.14.421
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