Biquotients with singly generated rational cohomology
Vitali Kapovitch, Wolfgang Ziller
TL;DR
This paper classifies biquotients with rational cohomology generated by a single element and shows that the Gromoll-Meyer 7-sphere is uniquely realizable as such a biquotient among exotic spheres.
Contribution
It provides a complete classification of biquotients with singly generated rational cohomology and identifies the Gromoll-Meyer 7-sphere as the only exotic sphere with this property.
Findings
Gromoll-Meyer 7-sphere is the only exotic sphere that can be expressed as a biquotient.
All biquotients with rational cohomology generated by one element are classified.
The classification links the topology of biquotients to their rational cohomology structure.
Abstract
We classify all biquotients whose rational cohomology rings are generated by one element. As a consequence we show that the Gromoll-Meyer 7-sphere is the only exotic sphere which can be written as a biquotient.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications