Positive curvature and rational ellipticity

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Simply connected manifolds of positive sectional curvature are speculated to have a rigid topological structure. In particular, they are conjectured to be rationally elliptic, ie to have only finitely many non-zero rational homotopy groups. In this article, we combine positive curvature with rational ellipticity to obtain several topological properties of the underlying manifold. These results include an upper bound on the Euler characteristic and new evidence for a couple of well-known conjectures due to Hopf and Halperin. We also prove a conjecture of Wilhelm for even-dimensional manifolds whose rational type is one of the known examples of positive curvature.

Original languageEnglish (US)
Article numberA011
Pages (from-to)2269-2301
Number of pages33
JournalAlgebraic and Geometric Topology
Volume15
Issue number4
DOIs
StatePublished - Oct 10 2015
Externally publishedYes

Fingerprint

Positive Curvature
Ellipticity
Rational Homotopy
Homotopy Groups
Euler Characteristic
Sectional Curvature
Topological Structure
Topological Properties
Upper bound

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Positive curvature and rational ellipticity. / Amann, Manuel; Kennard, Lee.

In: Algebraic and Geometric Topology, Vol. 15, No. 4, A011, 10.10.2015, p. 2269-2301.

Research output: Contribution to journalArticle

Amann, Manuel ; Kennard, Lee. / Positive curvature and rational ellipticity. In: Algebraic and Geometric Topology. 2015 ; Vol. 15, No. 4. pp. 2269-2301.
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