Abstract: One of the meta questions on mapping class groups concerns understanding the similarities and differences between mapping class groups and arithmetic groups. By work of Harer and Borel—Serre, both mapping class groups and arithmetic groups exhibit a twisted form of Poincare duality. I will review the construction of their dualizing modules in terms of curve complexes and Tits buildings. These duality results have proven to be very useful for computing high dimensional cohomology groups. The Torelli map between mapping class groups and symplectic groups gives maps on group homology. However, it does not seem to induce a map on dualizing modules. I will describe a replacement for the symplectic Tits building called the algebraic curve complex that does have a natural map from the curve complex. In joint work with Sroka and Scalamadre, we prove that the algebraic curve complex is a form of Harrison homology of the symplectic Tits buildings. This gives new insights into why the Church—Farb—Putman vanishing conjectures appear to be true for arithmetic groups but is false for mapping class groups (a result of Chan—Galatius—Payne). It also supplies a new perspective on work of Fullarton—Putman on the cohomology of congruence subgroups of mapping class groups. From the perspective of moduli spaces, this is conjecturally related to the fact that the map from M_g to A_g is not proper but becomes proper after removing the locus of products.