Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups

Xie, Xue‐Jun

doi:10.1112/jtopol/jtu023

Search citation statements

Order By: Relevance

Paper Sections

Select...

Heintze Groups1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

2022

Publication Types

Select...

Article3

Other2

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, it is proved in the case of Heintze groups of Carnot type ( [Pan89]) and for groups of the form R n ⋊ α R ( [Xie14]). See also [Pan08,SX12,Xie15a,Xie15b,CS17] for related results and particular cases.…”

Section: Heintze Groupsmentioning

confidence: 99%

Relative $L^p$-cohomology and Heintze groups

Sequeira¹

2019

Preprint

View full text Add to dashboard Cite

We define the L p -cohomology of a Gromov hyperbolic Riemannian manifold relative to a point on its boundary at infinity and prove that it is, as in the classical case, a quasi-isometry invariant. We obtain an application to the problem of quasi-isometry classification of Heintze groups. More precisely, we explicitly construct non-zero relative L p -cohomology classes on a Heintze group R n ⋊ α R, which allows us to prove that the eigenvalues of α, up to a scalar multiple, are invariants under quasi-isometries.

show abstract