Moduli space with a boundary

Simple Type and the Boundary of Moduli Space

We measure, in two distinct ways, the extent to which the boundary region of moduli space contributes to the “simple type” condition of Donaldson theory. Using a geometric representative of μ(pt), the boundary region of moduli space contributes 6/64 of the homology required for simple type, regardless of the topology or geometry of the underlying 4-manifold. The simple type condition thus reduc...

The Boundary of the Moduli Space of Quadratic Rational Maps

Let M2 be the space of quadratic rational maps f : P 1 → P , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification X of M2 is defined, as a modification of Milnor’s M2 ≃ CP , by choosing representatives of a conjugacy class [f ] ∈ M2 such that the measure of maximal entropy of f has conformal barycenter at the origin in R, and taking the closu...

Navigating moduli space with complex twists

We discuss a common framework for studing twists of Riemann surfaces coming from earthquakes, Teichmüller theory and Schiffer variations, and use it to analyze geodesics ins the moduli space of isoperiodic 1-forms.

The Moduli Space of Surfaces with K

Moduli space parametrizations

This is the second of two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R .S S/ as defined by a certain natural pair of almost complex structure and symplectic form. The first article in this series described the local structure of the moduli spaces and gave existence theorems. This article describes a stratification of the moduli spaces and gives ...