Back to Search
Start Over
On the realizability of group actions.
- Source :
-
Advances in Mathematics . Oct2018, Vol. 336, p299-315. 17p. - Publication Year :
- 2018
-
Abstract
- Let the pair ( G , M ) R denote a group G acting on an R -module M , R a unitary ring. We ask for the existence of an R -local space X such that ( E ( X ) , π k ( X ) ) R is equivalent, in a natural way, to ( G , M ) R , for some k ≥ 2 , where E ( X ) denotes the group of homotopy classes of self-homotopy equivalences of X . If such an X exists, we say that X realizes the group action ( G , M ) R . We prove that if G is finite and acts faithfully on a finitely generated Q -module M , there exist infinitely many rational spaces realizing ( G , M ) Q . Our proof relies on providing a positive answer to Kahn's realizability problem for a large class of orthogonal groups that strictly contains finite ones. As a matter of fact, we enlarge the class of groups that is known to be realizable in the classical Kahn's sense. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 336
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 131402166
- Full Text :
- https://doi.org/10.1016/j.aim.2018.07.034