Higher Morse moduli spaces and $n$-categories

Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on Morse-Bott techniques for Floer trajectories. Our main motivation is to understand the relationship between linearized contact homology of a fillable contact m...

2 8 N ov 2 00 5 Moduli spaces of local systems and higher Teichmüller theory

Moduli Spaces of Higher Spin Curves and Integrable Hierarchies

We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to GelfandDickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a generating function which yields a solution of the semiclassical limit of the KdVr equations. We formulate axioms for a cohomology class on this moduli space wh...

Higher Genus Moduli Spaces in Closed String Field Theory

We provide an overview of covariant closed string field theory, covering briefly the geometry of moduli spaces of Riemann surfaces, conformal field theory in the operator formalism and the Batalin-Vilkovisky formalism. Several important applications are also described including connections on the space of conformal theories, quantum background independence, the ghost-dilaton theorem, and string...

Extremal Higher Codimension Cycles on Moduli Spaces of Curves

We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli spaceMg,n of stable genus g curves with n ordered marked points. In particular, we prove that codimension two boundary strata are extremal and exhibit extremal boundary strata of higher codimension. We also show that the locus of hyperelliptic curves with a marked Weierstrass po...