Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 1 (2014), 421-438.
Rational analogs of projective planes
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.
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 421-438.
Received: 15 October 2010
Revised: 22 July 2013
Accepted: 22 July 2013
First available in Project Euclid: 19 December 2017
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Su, Zhixu. Rational analogs of projective planes. Algebr. Geom. Topol. 14 (2014), no. 1, 421--438. doi:10.2140/agt.2014.14.421. https://projecteuclid.org/euclid.agt/1513715807