Geometry and Topology
Speaker: Alex Suciu (Northeastern University)
"Koszul linearization and invariants of non-formal cdga models"
Time: 14:00 - 15:00
Room: MC 107
I will present a method for computing resonance varieties,
Alexander invariants, and Chen ranks of spaces that are not formal
but admit finite-type cdga models. The method is based on Koszul
linearization, which replaces the classical algebraic constructions
underlying Alexander-type invariants with functorial algebraic objects
built directly from the cdga, thereby shifting the role of the
cohomology ring to the full model.
A key feature of this approach is the existence of functorial spectral
sequences that interpolate between invariants computed from cohomology
and those arising from the cdga model, with higher differentials
encoding iterated Massey products. This framework yields extensions of
several results from the formal setting, including the fact that
cohomology controls the first-order behavior at the origin of the
resonance varieties, as well as explicit formulas for infinitesimal
Alexander invariants and Chen ranks in terms of the model.
Discrepancies between cohomological and model-theoretic
invariants thus provide computable obstructions to formality.
The constructions are functorial with respect to cdga morphisms
and provide effective tools for computation. Applications include
nilpotent Lie algebras and elliptic configuration spaces, as well
as consequences for detecting non-formality.