On the torus cobordant cohomology spheres


Ozkurt A. A. , DÖNMEZ D.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.119, ss.101-108, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 119 Konu: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s12044-009-0010-7
  • Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Sayfa Sayıları: ss.101-108

Özet

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 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 Z-cohomology) must be linearly equivalent. As a corollary, for connected case, we prove a variant of Smith's question.