Journal of Symplectic Geometry

Volume 13 (2015)

Number 2

Factorizations in $SL(2, \mathbb{Z})$ and simple examples of inequivalent Stein fillings

Pages: 261 – 277



Denis Auroux (Department of Mathematics, University of California at Berkeley)


We give simple examples of elements of $SL(2, \mathbb{Z})$ admitting inequivalent factorizations into products of Dehn twists. This can be interpreted in terms of inequivalent Stein fillings of the same contact $3$-manifold by genus $1$ Lefschetz fibrations over the disk.

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