By Kyung Bai Lee
Seifert fiberings expand the inspiration of fiber package deal mappings by means of permitting many of the fibers to be singular. clear of the singular fibers, the fibering is a standard package with fiber a hard and fast homogeneous house. The singular fibers are quotients of this homogeneous area by way of individual teams of homeomorphisms. those fiberings are ubiquitous and demanding in arithmetic. This booklet describes in a unified means their constitution, how they come up, and the way they're categorised and utilized in functions. Manifolds owning such fiber constructions are mentioned and diversity from the classical third-dimensional Seifert manifolds to better dimensional analogues encompassing, for instance, flat manifolds, infra-nil-manifolds, area types, and their moduli areas. the mandatory instruments now not coated in easy graduate classes are handled in huge aspect. those comprise transformation teams, cohomology of teams, and wanted Lie concept. Inclusion of the Bieberbach theorems, life, forte, and stress of Seifert fiberings, aspherical manifolds, symmetric areas, toral rank of round house varieties, equivariant cohomology, polynomial constructions on solv-manifolds, fastened aspect concept, and different examples, workouts and functions attest to the breadth of those fiberings. this is often the 1st time the scattered literature on singular fiberings is introduced jointly in a unified strategy. the recent tools and instruments hired might be important to researchers and scholars drawn to geometry and topology.
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