“Arnold’s trinities” refers to a metamathematical observation of Vladimir Arnold that many interesting mathematical concepts and theories occur in triples, with some hidden influence of ℝ/ℂ/ℍ hidden in the background. By algebraic 2d gravitation theory I mean a very rich system of interrelated algebraic structures surrounding the concept of cohomological field theory in genus 0. It appears that there is an Arnold trinity of algebraic 2d gravitation theories (and one of them is a very natural non-commutative version of a CohFT), and I’ll try to expose them, with a special focus on new homotopy quotients statements that we discovered last year.
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