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Coronae of product spaces and the Coarse Baum-Connes conjecture

Tomohiro Fukaya, Shin-ichi Oguni

Abstract

We study the coarse Baum-Connes conjecture for product spaces and product groups. We show that a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy some assumptions on peripheral subgroups, satisfies the coarse Baum-Connes conjecture. For this purpose, we construct and analyze an appropriate compactification and its boundary, "corona", of a product of proper metric spaces.

Coronae of product spaces and the Coarse Baum-Connes conjecture

Abstract

We study the coarse Baum-Connes conjecture for product spaces and product groups. We show that a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy some assumptions on peripheral subgroups, satisfies the coarse Baum-Connes conjecture. For this purpose, we construct and analyze an appropriate compactification and its boundary, "corona", of a product of proper metric spaces.

Paper Structure

This paper contains 25 sections, 91 equations.

Table of Contents

  1. Introduction
  2. Compactification at infinity
  3. Compactification at infinity
  4. Corona and coarse compactification
  5. Corona of a product space
  6. Join
  7. Embedding of a product space
  8. Higson functions
  9. Corona of Busemann spaces and open cones
  10. Busemann spaces
  11. Open cone
  12. Contractibility of the compactification at infinity of a product space
  13. Construction of $H$
  14. Continuity at $W_1\star \dots \star W_n \times [0,\infty)$
  15. Continuity at $W_1\star \dots \star W_n \times \{\infty\}$
  16. ...and 10 more sections

Theorems & Definitions (24)

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  • ...and 14 more