This item is non-discoverable
Loading...
Non-discoverable
Spectrally similar incommensurable 3-manifolds
Futer, D Millichap, C
Futer, D
Millichap, C
Citations
Altmetric:
Genre
Pre-print
Date
2017-08-01
Advisor
Committee member
Group
Department
Permanent link to this record
Collections
Research Projects
Organizational Units
Journal Issue
DOI
10.1112/plms.12045
Abstract
© 2017 London Mathematical Society. Reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable. Building toward a negative answer to this question, we construct examples of hyperbolic 3-manifolds that share an arbitrarily large portion of the length spectrum but are not commensurable. More precisely, for every n≫0, we construct a pair of incommensurable hyperbolic 3-manifolds Nn and Nnμ whose volume is approximately n and whose length spectra agree up to length n. Both Nn and Nnμ are built by gluing two standard submanifolds along a complicated pseudo-Anosov map, ensuring that these manifolds have a very thick collar about an essential surface. The two gluing maps differ by a hyper-elliptic involution along this surface. Our proof also involves a new commensurability criterion based on pairs of pants.
Description
Citation
Citation to related work
Wiley
Has part
Proceedings of the London Mathematical Society
ADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu