Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/0608418

Crosscap Numbers of Two-component Links

Gengyu Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.

Explore related subjects

math.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gengyu Zhang. 2006-08-16. Crosscap Numbers of Two-component Links. https://arxiv.org/abs/math/0608418

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

KEEP EXPLORING

Related papers

arXiv2026

Relationship between quandle shadow cocycle invariants and Vassiliev invariants

As one of the problems in his list [20], T. Ohtsuki proposed to study relations between quandle cocycle invariants and quantum invariants. The aim of this paper is to answer one of those questions. We prove that the coefficient of the finite perturbative expansion of the quandle shadow cocycle invariant defined by $(\Z /p\Z)$-Laurent polynomial quandle is Vassiliev invariant for any braids.

math.GT↗
arXiv2026

Holed cone structures on 3-manifolds

We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.

math.GT↗