کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904607 | 1633752 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the realizability of group actions
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
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),Ïk(X))R is equivalent, in a natural way, to (G,M)R, for some kâ¥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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 336, 1 October 2018, Pages 299-315
Journal: Advances in Mathematics - Volume 336, 1 October 2018, Pages 299-315
نویسندگان
Cristina Costoya, Antonio Viruel,