On dimensions supporting a rational projective plane

Lee Kennard, Zhixu Su

Research output: Contribution to journalArticle

Abstract

A rational projective plane ((Formula presented.)) is a simply connected, smooth, closed manifold (Formula presented.) such that (Formula presented.). 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 (Formula presented.). We then confirm the existence of a (Formula presented.) 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)1-21
Number of pages21
JournalJournal of Topology and Analysis
DOIs
StateAccepted/In press - Jan 1 2017
Externally publishedYes

Keywords

  • characteristic classes
  • Rational projective planes
  • rational surgery realization

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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