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Title: On dimensions supporting a rational projective plane
A rational projective plane ([Formula: see text]) is a simply connected, smooth, closed manifold [Formula: see text] such that [Formula: see text]. 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: see text]. We then confirm the existence of a [Formula: see text] 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.  more » « less
Award ID(s):
1904354
PAR ID:
10110783
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Topology and Analysis
ISSN:
1793-5253
Page Range / eLocation ID:
1 to 21
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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