A characterization of spherical polyhedron surfaces

Feng Luo

Home/Archive/arXiv

arXiv · math/0408112

A characterization of spherical polyhedron surfaces

Feng Luo

View original source ↗Read source document ↗Export metadata ↓

Abstract

A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedron surfaces in terms of the triangulation and the angle assignment is established.

Explore related subjects

math.GT math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Feng Luo. 2006-03-28. A characterization of spherical polyhedron surfaces. https://arxiv.org/abs/math/0408112

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Burau representation of the braid group is faithful for n = 4

In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.

math.GT↗

arXiv2026

A counterexample to the wrapping number conjecture

We exhibit an annular knot with wrapping number four whose Kauffman bracket has annular degree at most two. This disproves the wrapping number conjecture.

math.GT↗

arXiv2026

The Lorenz braid index and hyperbolic volume

A result of Futer, Kalfagianni, and Purcell implies that an upper volume bound for all link complements in the 3-sphere cannot depend solely on the braid index. In this paper, we introduce the Lorenz braid index and generalise the bunch algorithm to provide a general upper volume bound for all link complements in the 3-sphere. Such an upper bound is a quadratic polynomial in the Lorenz braid index. In addition, we construct an explicit family of hyperbolic Lorenz knots for which the classical braid index and the Seifert genus both tend to infinity, while the Lorenz braid index remains bounded.

math.GT↗