A smooth k-web is a family of k distinct smooth foliations whose
leaves intersect generically. Objects of this kind have been
thoroughly studied in the setting of algebraic and symplectic
geometry. During the talk we will focus on the less-traveled
route: webs in the geometry of volume-preserving maps.
These unimodular webs possess nontrivial local structure, which
manifests itself in the existence of curvature - a symmetric
2-tensor covariant with respect to volume-preserving
web-equivalences, named after its classical counterpart defined
by Thomsen and Blaschke in the 1920s. This structure can also
be described by means of a natural affine connection determined
uniquely by the structure of a given web and a choice of the
volume form on the ambient space.
Our main goal is to construct this connection, and to relate its
curvature to the curvature of the web in order to establish
another criterion for its triviality.