Reflective anisotropic hyperbolic lattices of rank 4

Богачев, Николай Владимирович; Nikolay, Bogachev,

doi:10.4213/rm9756

Uspekhi Mat. Nauk

2017

DOI: 10.4213/rm9756

|View full text |Cite

Reflective anisotropic hyperbolic lattices of rank 4

Николай Владимирович Богачев¹,

Bogachev, Nikolay²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2018

2023

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 6 publications

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

Nikolay

2022

Transformation Groups

View full text Add to dashboard Cite

In 1974, Kaplinskaja classified all simplicial straight hyperbolic Coxeter prisms. In this paper, we determine precisely which of these prisms are properly quasi-arithmetic or arithmetic. We also present some observations regarding commensurability classes and systoles of the associated orbifolds. Finally, we show that there is a cocompact properly quasi-arithmetic reflection group in H 3 preserving an isotropic quadratic form. This phenomenon was previously known due to Vinberg only in dimension 2.

show abstract

From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

Nikolay

2022

Transformation Groups

View full text Add to dashboard Cite

show abstract

Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

Nikolay¹

2019

Izv. Math.

View full text Add to dashboard Cite

Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes

Alexandrov

2023

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

In this paper we study × 0 \times _0 -products of Lannér diagrams. We prove that every × 0 \times _0 -product of at least four Lannér diagrams with at least one diagram of order ≥ 3 \geq 3 is superhyperbolic. As a corollary, we obtain that known classifications exhaust all compact hyperbolic Coxeter polytopes that are combinatorially equivalent to products of simplices. We also consider compact hyperbolic Coxeter polytopes whose every Lannér subdiagram has order 2 2 . The second result of this paper slightly improves recent Burcroff’s upper bound on the dimension of such polytopes to 12 12 .

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Reflective anisotropic hyperbolic lattices of rank 4

Cited by 6 publications

References 5 publications

From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes

Contact Info

Product

Resources

About