Automorphisms of manifolds

By Michael Weiss, B. Williams. 2000

55 citations recorded by the source corpus.

This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias concordance theory, Waldhausen style. It culminates in (an outline of) a synthesis of these two theories, producing algebraic models, valid in a stable range, for spaces of manifolds in a fixed homotopy type. This is inspired by earlier work of Burghelea-Lashof and Hatcher. The algebraic models are a mix of algebraic L-theory and algebraic K-theory.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b36c4ede4d938a4af22eaf0e4e080e6040079a9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. W. Lück
2. H. Reich
3. Ryan Budney
4. Arthur Bartels
5. M. Kreck

In Geometry and Topology

1. H. Reich
2. W. Lück
3. Ryan Budney
4. Arthur Bartels
5. Christian Wegner
6. Dev Sinha
7. Hanfeng Li
8. Michael W. Davis

In Mathematical Physics

1. W. Lück
2. H. Reich
3. Arthur Bartels
4. Ryan Budney
5. Christian Wegner
6. Dev Sinha
7. Hanfeng Li
8. Michael W. Davis

Citations in the corpus

• A family of embedding spaces (2006, background): “The terminology of ‘degree’ comes from the pseudoisotopy theory of discs and spheres [4, 5, 84, 25].”
• The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, background): “For a modern survey on automorphisms of manifolds we refer to [329].”