Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

Translation covers of some triply periodic Platonic surfaces


Authors: Jayadev S. Athreya and Dami Lee
Journal: Conform. Geom. Dyn. 25 (2021), 34-50
MSC (2020): Primary 32G15, 57K20
DOI: https://doi.org/10.1090/ecgd/357
Published electronically: April 2, 2021
MathSciNet review: 4238630
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study translation covers of several triply periodic polyhedral surfaces that are intrinsically Platonic. We describe their affine symmetry groups and compute the quadratic asymptotics for counting saddle connections and cylinders, including the count of cylinders weighted by area. The mathematical study of triply periodic surfaces was initiated by Novikov, motivated by the study of electron transport. The surfaces we consider are of particular interest as they admit several different explicit geometric and algebraic descriptions, as described, for example, in the second author’s thesis.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2020): 32G15, 57K20

Retrieve articles in all journals with MSC (2020): 32G15, 57K20


Additional Information

Jayadev S. Athreya
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
MR Author ID: 663249
ORCID: 0000-0002-9317-6229
Email: jathreya@uw.edu

Dami Lee
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
MR Author ID: 1229078
ORCID: 0000-0001-5924-4171
Email: damilee@uw.edu

Received by editor(s): December 18, 2019
Received by editor(s) in revised form: September 22, 2020, and October 22, 2020
Published electronically: April 2, 2021
Additional Notes: The second author was supported by NSF Grant No. DMS-1440140
Article copyright: © Copyright 2021 American Mathematical Society