In this paper we discuss Kfinneth decompositions for finite quotients of several classes of smooth projective varieties. The main result is the existence o f an explicit (and readily computable) Chow-Kiinneth decomposition in the sense o f Murre with several pleasant properties for finite quotients of abelian varieties. This applies in particular to symmetric products of abelian varieties and a...

We investigate the modular group as a finitely presented group. It has a large collection of interesting quotients. In 1987 Conder substantially identified the onerelator quotients of the modular group which are defined using representatives of the 300 inequivalent extra relators with length up to 24. We study all such quotients where the extra relator has length up to 36. Up to equivalence, th...

A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...

An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexi...

Quotienting by simulation equivalences is awell-established technique for reducing the size of nondeterministic Büchi automata.We adapt this technique to alternating Büchi automata. To this end we suggest two new quotients, namely minimax and semi-elective quotients, prove that they preserve the recognized languages, and show that computing them is not more difficult than computing quotients fo...

We propose an approach via Frobenius manifolds to the study (began in [BCK2]) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding “abelianized” quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonab...

We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum size and then contract. Maldacena's conjecture suggests that they should be represented in string theory by suitable quotients of the boundary conformal eld theory. We discuss the required identi ca...

We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum size and then contract. Maldacena’s conjecture suggests that they should be represented in string theory by suitable quotients of the boundary conformal field theory. We discuss the required identif...

Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to groups of Weil divisors generating the topology. Groups comprising Cartier divisors define free quotients, whereas Q-Cartier divisors define geometric quotients. Each quotient presentation yields homogeneous coordinates. ...