6 papers
The transverse singular complex
Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha
Let be a smooth manifold without boundary and let be a countable collection of manifolds with corners, each equipped with a smooth map to . We show that the si…
Foundations of geometric cohomology: from co-orientations to product structures
Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with…
Operadic Calculus for Higher Colour-Kinematics Duality
Anibal M. Medina-Mardones, Bruno Vallette
The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred…
Framed Polytopes and Higher Categories
Guillaume Laplante-Anfossi, Anibal M. Medina-Mardones, Arnau Padrol
In the early 1990s, Kapranov and Voevodsky proposed a geometric method for constructing higher-categorical pasting diagrams from generically framed convex polytopes. This work revi…
What makes math problems hard for reinforcement learning: a case study
Ali Shehper, Anibal M. Medina-Mardones, Lucas Fagan +6
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high…
Adams' cobar construction as a monoidal -coalgebra model of the based loop space
Anibal M. Medina-Mardones, Manuel Rivera
We prove that the classical map comparing Adams' cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-iso…