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Integral structure of the skein algebra of the 5-punctured sphere

Haimiao Chen

Abstract

We give an explicit presentation for the Kauffman bracket skein algebra of the $5$-punctured sphere over any commutative unitary ring.

Integral structure of the skein algebra of the 5-punctured sphere

Abstract

We give an explicit presentation for the Kauffman bracket skein algebra of the -punctured sphere over any commutative unitary ring.
Paper Structure (5 sections, 4 theorems, 15 equations, 4 figures)

This paper contains 5 sections, 4 theorems, 15 equations, 4 figures.

Table of Contents

  1. Introduction
  2. A presentation for $\mathcal{S}_4$
  3. Useful identities
  4. Relations
  5. Statement and proof

Key Result

Theorem 1.1

The skein algebra $\mathcal{S}_{n}$ is generated by $\mathfrak{T}_n$, and the ideal of defining relations is $\mathcal{I}_n$.

Figures (4)

  • Figure 1: The surface $\Sigma_{0,4+1}$; the dotted lines are $\gamma_j$, $j=1,\ldots,4$.
  • Figure 2: Computing $t_{123\overline{2}}t_{13}$.
  • Figure 3: Computing $t_{23}t_{12\overline{4}34}$.
  • Figure :

Theorems & Definitions (7)

  • Theorem 1.1: Ch22 Section 5
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Theorem 2.3
  • proof