Löh, Clara: l 1 -homology and simplicial volume : l1-homology and simplicial volume. 2007
Inhalt
- Introduction
- Contents
- Homology of normed chain complexes
- l¹-Homology and bounded cohomology
- l¹-Homology of spaces
- l¹-Homology of discrete groups
- l¹-Homology of spaces with twisted coefficients
- Peeking into the mirror universe
- Duality
- Isomorphisms in l¹-homology
- Isomorphisms in l¹-homology of spaces
- Isomorphisms in l¹-homology of discrete groups
- l¹-Homology of spaces via projective resolutions
- Example application -- a generalised straightening
- Simplicial volume and l¹-homology
- Fundamental cycles of manifolds
- Definition of simplicial volume
- Computing simplicial volume
- A collection of properties of simplicial volume
- A finiteness criterion for simplicial volume
- Stating the finiteness criterion
- l¹-Invisibility and the proof of the finiteness criterion
- A closer look at l¹-invisible manifolds
- Applying the finiteness criterion
- Homological algebra of Banach G-modules
- Relatively injective and relatively projective Banach G-modules
- Relatively injective and relatively projective resolutions
- Bounded cohomology with twisted coefficients
- Gromov's duality principle for non-compact manifolds
- Statement of the non-compact duality principle
- The homological version
- The dual point of view
- A generalised product formula
- Measure homology and measure l¹-homology
- Bibliography
- Table of notation
- Index