# Average four-genus of two-bridge knots

## TL;DR

This paper demonstrates that for two-bridge knots, the ratio of the smooth four-genus to the Seifert genus approaches zero as the crossing number increases, revealing a diminishing relationship between these invariants.

## Contribution

It establishes a new asymptotic result linking the smooth four-genus and Seifert genus for two-bridge knots as crossing numbers grow large.

## Key findings

- Expected ratio tends to zero with increasing crossing number
- Shows asymptotic behavior of genus invariants in two-bridge knots
- Provides insight into the relationship between smooth four-genus and Seifert genus

## Abstract

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.