Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category is an equivalence class of composable sequences of canonical relations, with composition given by concatenation. In this note, we show that every such morphism is represented by a sequence consisting of just two relations, one of them a reduction and the other a coreduction.

We extend the notion of the cardinality of a discrete groupoid (equal to the Euler characteristic of the corresponding discrete orbifold) to the setting of Lie groupoids. Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associated stack rather than of the groupoid itself. Since there is no natural measure in the smooth case like the counting measure in the discrete case, we need extra data to define the volume. This data has the form of an invariant section of a natural line bundle over the base of the groupoid. Invariant sections of a square root of this line bundle constitute an “intrinsic Hilbert space” of the stack.

In this paper we study associative algebras with a Poisson algebra structure
on the center acting by derivations on the rest of the algebra. These
structures, which we call Poisson fibred algebras, appear in the study of
quantum groups at roots of 1 and related algebras, as well as in the
representation theory of affine Lie algebras at the critical level. Poisson
fibred algebras lead to a generalization of Poisson geometry, which we develop
in the paper. We also take up the general study of noncommutative spaces which
are close to enough commutative ones so that they contain enough points to have
interesting commutative geometry. One of the most striking uses of our
noncommutative spaces is the quantum Borel-Weil-Bott Theorem for quantum sl_q
(2) at a root of unity, which comes as a calculation of the cohomology of
actual sheaves on actual topological spaces.

Ferry service between the East Bay and San Francisco is one of the most tangible, in the view of some most positive, legacies of the Loma Prieta Earthquake. Begun as an emergency measure within hours of the event, the service has continued in one form or another through the time of this writing, and in the current political climate is likely to continue indefinitely.

Several studies of East Bay ferry service have been carried out over the past decade. These have probed the demand for and costs of ferry service, and developed plans for incorporating it into the Bay Area's transport system. This paper has a different objective -- to narrate and analyze the events surrounding the birth of the ferry service and its transformation from an emergency response to a seemingly permanent fixture.

The investigation consisted of two parts. Supply side developments were followed through systematic reading of pertinent media stories and analysis of fares and schedules. Section 2 discusses this aspect of the research. Demand for ferry service was tracked through a series of three passenger surveys, results of which are discussed in Section 3. Section 4 offers conclusions.