## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 10, Number 3 (2006), 317-343.

### The vertex on a strip

Amer Iqbal and Amir-Kian Kashani-Poor

#### Abstract

We demonstrate that for a broad class of local Calabi--Yau geometries built around a string of $\I\mathbb{P}^1$'s — those whose toric diagrams are given by triangulations of a strip — we can derive simple rules, based on the topological vertex, for obtaining expressions for the topological string partition function in which the sums over Young tableaux have been performed. By allowing non-trivial tableaux on the external legs of the corresponding web diagrams, these strips can be used as building blocks for more general geometries. As applications of our result, we study the behavior of topological string amplitudes under flops, as well as check Nekrasov's conjecture in its most general form.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 10, Number 3 (2006), 317-343.

**Dates**

First available in Project Euclid: 30 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1154236379

**Mathematical Reviews number (MathSciNet)**

MR2250273

**Zentralblatt MATH identifier**

1131.14045

#### Citation

Iqbal, Amer; Kashani-Poor, Amir-Kian. The vertex on a strip. Adv. Theor. Math. Phys. 10 (2006), no. 3, 317--343. https://projecteuclid.org/euclid.atmp/1154236379