Algebraic & Geometric Topology

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.

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 421-438.

Dates
Received: 15 October 2010
Revised: 22 July 2013
Accepted: 22 July 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715807

Digital Object Identifier
doi:10.2140/agt.2014.14.421

Mathematical Reviews number (MathSciNet)
MR3158765

Zentralblatt MATH identifier
1291.57019

Subjects
Primary: 57R20: Characteristic classes and numbers
Secondary: 57R65: Surgery and handlebodies 57R67: Surgery obstructions, Wall groups [See also 19J25]

Keywords
rational surgery rational homotopy type smooth manifold

Citation

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


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