Skip to main content
MathOverflow

Return to Question

added 229 characters in body
Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

What is an example of a torsion free discrete abelian group $G$ whose dual space $\hat{G}$ is not a path connected space?

The Motivation: The motivation comes from the idempotent conjecture of Kaplanski: For a torsion free and discreet abelian group $G$ the dual group $\hat{G}$ is a connected space so $C^*_{red} G \sim C(\hat{G})$ has no nontrivial idempotent. So inThus in this case the Kaplanski conjecture is true so this situation is a motivation for belife on idempotent conjecture of Kaplanski. So(See the first pages of "An introduction to the Baum Connes conjecture" by Alain Valette. So we wish to reduce the power of connectivity as much as possible with a possible hope of having counter example. For example we would like to think to a possible discrete group $G$ which is torsion free and some of its reasonable dual or other types of dual or this one would be weak connected as much as possible.

What is an example of a torsion free discrete abelian group $G$ whose dual space $\hat{G}$ is not a path connected space?

The Motivation: The motivation comes from the idempotent conjecture of Kaplanski: For a torsion free and discreet abelian group $G$ the dual group $\hat{G}$ is a connected space so $C^*_{red} G \sim C(\hat{G})$ has no nontrivial idempotent. So in this case the Kaplanski conjecture is true. So we wish to reduce the power of connectivity as much as possible. For example we would like to think to a possible discrete group $G$ which is torsion free and some of its reasonable dual or other types of dual or this one would be weak connected as much as possible.

What is an example of a torsion free discrete abelian group $G$ whose dual space $\hat{G}$ is not a path connected space?

The Motivation: The motivation comes from the idempotent conjecture of Kaplanski: For a torsion free and discreet abelian group $G$ the dual group $\hat{G}$ is a connected space so $C^*_{red} G \sim C(\hat{G})$ has no nontrivial idempotent. Thus in this case the Kaplanski conjecture is true so this situation is a motivation for belife on idempotent conjecture of Kaplanski.(See the first pages of "An introduction to the Baum Connes conjecture" by Alain Valette. So we wish to reduce the power of connectivity as much as possible with a possible hope of having counter example. For example we would like to think to a possible discrete group $G$ which is torsion free and some of its reasonable dual or other types of dual or this one would be weak connected as much as possible.

Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Idempotent conjecture and (weak) connectivity of (a reasonable) dual group

What is an example of a torsion free discrete abelian group $G$ whose dual space $\hat{G}$ is not a path connected space?

The Motivation: The motivation comes from the idempotent conjecture of Kaplanski: For a torsion free and discreet abelian group $G$ the dual group $\hat{G}$ is a connected space so $C^*_{red} G \sim C(\hat{G})$ has no nontrivial idempotent. So in this case the Kaplanski conjecture is true. So we wish to reduce the power of connectivity as much as possible. For example we would like to think to a possible discrete group $G$ which is torsion free and some of its reasonable dual or other types of dual or this one would be weak connected as much as possible.