Topological spherical space form problem. III. Dimensional bounds and smoothing

Topological Spherical Space Forms

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a survey of some of the main results and a guide to the literature.

A Four-manifold Approach to the Spherical Space Form Problem

For certain 3-manifolds M with finite fundamental group, we construct smooth, negative definite 4-manifolds, with boundary containingM and some orthogonal spherical spaces forms. This allows a translation of the existence problem for finite fundamental groups of 3-manifolds into a problem in equivariant gauge theory.

Moduli Space of Topological 2-form Gravity

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space. e-mail: [email protected]...

The Double Bubble Problem in Spherical Space and Hyperbolic Space

Harmonic Morphisms from Three-dimensional Euclidean and Spherical Space Forms

This paper gives a description of all harmonic morphisms from a threedimensional non-simply-connected Euclidean and spherical space form to a surface, by extending the work of Baird-Wood [4, 5] who dealt with the simply-connected case; namely we show that any such harmonic morphism is the composition of a “standard” harmonic morphism and a weakly conformal map. To complete the description we li...