Rational analogs of projective planes

Su, Zhixu

doi:10.2140/agt.2014.14.421

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Rational analogs of projective planes

Zhixu Su

Algebraic & Geometric Topology 14 (2014) 421–438

DOI: 10.2140/agt.2014.14.421

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.

Keywords

rational surgery, rational homotopy type, smooth manifold

Mathematical Subject Classification 2010

Primary: 57R20

Secondary: 57R65, 57R67

References

Publication

Received: 15 October 2010

Revised: 22 July 2013

Accepted: 22 July 2013

Published: 9 January 2014

Authors

Zhixu Su
Department of Mathematics University of California, Irvine Irvine, CA 92697 USA
http://www.math.uci.edu/people/zhixu-su

Volume 14, issue 1 (2014)