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arXiv · 1010.3274

Rational analogs of projective planes

Zhixu Su
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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.

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Zhixu Su. 2014-01-17. Rational analogs of projective planes. https://doi.org/10.2140/agt.2014.14.421

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