On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines

© Scuola Normale Superiore Pisa 2012. We compute the simplified presentations of the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the resulting groups turn out to be big.