The Hilali Conjecture for hyperelliptic spaces
Javier Fernandez de Bobadilla, Javier Fresan, Vicente Mu\~noz, and, Aniceto Murillo
TL;DR
This paper proves the Hilali Conjecture for hyperelliptic spaces, a class of elliptic spaces, confirming that their rational homotopy dimension does not exceed their rational homology dimension.
Contribution
It provides the first proof of the Hilali Conjecture for hyperelliptic elliptic spaces, expanding the class of spaces where the conjecture holds.
Findings
Proof of the Hilali Conjecture for hyperelliptic spaces
Verification that rational homotopy dimension does not exceed rational homology dimension in this class
Advancement in understanding elliptic space properties
Abstract
The Hilali Conjecture predicts that for a simply-connected elliptic space, the total dimension of the rational homotopy does not exceed that of the rational homology. Here we give a proof of this conjecture for a class of elliptic spaces known as hyperelliptic.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory