Consider a finite triangulation of surface M genus g and assume that spin-less fermions populate the edges triangulation. The quantum dynamics such particles takes place inside algebra canonical anti-commutation relations (CAR). Following Kitaev’s work on toric models, we identify sub-algebra CAR generated by elements associated to triangles vertices We show any Hamiltonian drawn from this disp...

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

This paper brings together Dana Scott’s measure-based semantics for the propositional modal logic S4, and recent work in Dynamic Topological Logic. In a series of recent talks, Scott showed that the language of S4 can be interpreted in the Lebesgue measure algebra, M, or algebra of Borel subsets of the real interval, [0, 1], modulo sets of measure zero. Conjunctions, disjunctions and negations ...