The localization theorem for finite-dimensional compact group actions | Zendy

Ali Özkurt | Zendy; Mehmet Onat | Zendy

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The localization theorem for finite-dimensional compact group actions

Author(s) -

Ali Özkurt,

Mehmet Onat

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1609-47

Subject(s) - mathematics , compact group , abelian group , maximal torus , torus , pure mathematics , group (periodic table) , locally compact space , lie group , group action , discrete mathematics , lie algebra , geometry , fundamental representation , chemistry , organic chemistry , weight

The localization theorem is known for compact $G$-spaces, where $G$ is a compact Lie group. In this study, we show that the localization theorem remains true for finite-dimensional compact group actions, and Borel's fixed point theorem holds not only for torus actions but for arbitrary finite-dimensional compact connected abelian group actions.

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