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On the cohomology ring and upper characteristic rank of Grassmannian of oriented 3-planes

  • Somnath BasuEmail author
  • Prateep Chakraborty
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Abstract

In this paper we study the mod 2 cohomology ring of the Grasmannian \(\widetilde{G}_{n,3}\) of oriented 3-planes in \({\mathbb {R}}^n\). We determine the degrees of the indecomposable elements in the cohomology ring. We also obtain an almost complete description of the cohomology ring. This description allows us to provide lower and upper bounds on the cup length of \(\widetilde{G}_{n,3}\). As another application, we show that the upper characteristic rank of \(\widetilde{G}_{n,3}\) equals the characteristic rank of \(\widetilde{\gamma }_{n,3}\), the oriented tautological bundle over \(\widetilde{G}_{n,3}\) if n is at least 8.

Keywords

Oriented Grassmanian of three planes Upper characteristic rank Cup-length 

Mathematics Subject Classification

Primary 57R19 57R20 57T15 Secondary 55R20 55R25 

Notes

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2019

Authors and Affiliations

  1. 1.Indian Institute of Science Education and ResearchMohanpurIndia
  2. 2.Indian Institute of TechonologyKharagpurIndia

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