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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