Two examples of vanishing and squeezing in K₁
Resumen:
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K₁. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K₁; this follows from the well-known result of Bass, Heller and Swan.
| 2020 | |
| ANII - FCE_3_2018_1_148588 | |
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Assembly maps Controlled topology Bass-Heller-Swan theorem |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
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http://nyjm.albany.edu/j/2020/26-28.html
https://nyjm.albany.edu/ https://hdl.handle.net/20.500.12008/33743 |
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| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| Sumario: | Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K₁. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K₁; this follows from the well-known result of Bass, Heller and Swan. |
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