Large scale homology theories and geometry. (English) Zbl 0898.55006
Kazez, William H. (ed.), Geometric topology. 1993 Georgia international topology conference, August 2–13, 1993, Athens, GA, USA. Providence, RI: American Mathematical Society. AMS/IP Stud. Adv. Math. 2(pt.1), 522-569 (1997).
In this very large paper some homological methods which can be and have been applied to geometry, topology and group theory are described. The contents are as follows : 1. Definitions and examples. 2. \(HX_{*}\) and \(RX_{*}\). 3. Metric rigidity phenomena I (packing). 4. Metric rigidity phenomena II (topological rigidity). 5. Connection to large scale index theory. 6. Uniformly finite homology. 7. Applications of \(H^{uf}_{0}\). 8. Higher homology. 9. Index theory again. 10. Final remarks. References.
For the entire collection see [Zbl 0882.00042].
For the entire collection see [Zbl 0882.00042].
Reviewer: M.Anastasiei (Iaşi)
MSC:
| 55N35 | Other homology theories in algebraic topology |
