• Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/119/01/0101-0108

    • Keywords

       

      Equivariant cohomology; integral weight; Serre spectral sequence; cobordism.

    • Abstract

       

      Let 𝐺 be a compact Lie group. In 1960, P A Smith asked the following question: ``Is it true that for any smooth action of 𝐺 on a homotopy sphere with exactly two fixed points, the tangent 𝐺-modules at these two points are isomorphic?" A result due to Atiyah and Bott proves that the answer is `yes’ for $\mathbb{Z}_p$ and it is also known to be the same for connected Lie groups. In this work, we prove that two linear torus actions on $S^n$ which are 𝑐-cobordant (cobordism in which inclusion of each boundary component induces isomorphisms in $\mathbb{Z}$-cohomology) must be linearly equivalent. As a corollary, for connected case, we prove a variant of Smith’s question.

    • Author Affiliations

       

      Ali Özkurt1 Doğan Dönmez1

      1. Department of Mathematics, Çukurova University, 01330-Adana, Turkey
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.