## Gauge theory and the $A$-polynomial

J. Math. Sci. Univ. Tokyo
Vol. 12 (2005), No. 1, Page 105--110.

Collin, Olivier
Gauge theory and the $A$-polynomial
In this article, we explain how to use instanton Floer homology of various Dehn surgeries along knots in integer homology spheres to prove that their $A$-polynomial is non-trivial. In particular, we show that all non-trivial knots in $S^3$ have non-trivial $A$-polynomial.