On dimensions supporting a rational projective plane

Lee Kennard, Zhixu Su

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A rational projective plane (2) is a simply connected, smooth, closed manifold M such that H - (M;)[α](α3). An open problem is to classify the dimensions at which such a manifold exists. The Barge-Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori-Stong integrality conditions on the Pontryagin numbers. In this paper, we simplify these conditions and combine them with the signature equation to give a single quadratic residue equation that determines whether a given dimension supports a 2. We then confirm the existence of a 2 in two new dimensions and prove several non-existence results using factorization of the numerators of the divided Bernoulli numbers. We also resolve the existence question in the Spin case, and we discuss existence results for the more general class of rational projective spaces.

Original languageEnglish (US)
Pages (from-to)535-555
Number of pages21
JournalJournal of Topology and Analysis
Volume11
Issue number3
DOIs
StatePublished - Sep 1 2019
Externally publishedYes

Keywords

  • Rational projective planes
  • characteristic classes
  • rational surgery realization

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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