The integral cohomology ring of E_8/T^1E_7
Masaki Nakagawa
TL;DR
This paper computes the integral cohomology rings of the homogeneous space E_8/T^1E_7 and the related space E_8/E_7 using algebraic topology methods, providing explicit cohomological descriptions.
Contribution
It introduces a method to explicitly determine the integral cohomology rings of complex homogeneous spaces like E_8/T^1E_7 and E_8/E_7.
Findings
Explicit integral cohomology ring of E_8/T^1E_7
Integral cohomology of E_8/E_7 derived from the circle bundle
Application of Borel presentation and Toda's method
Abstract
We determine the integral cohomology ring of the homogeneous space E_8/T^1E_7 by the Borel presentation and a method due to Toda. Then using the Gysin exact sequence associated with the circle bundle S^1 -> E_8/E_7 -> E_8/T^1E_7, we also determine the integral cohomology of E_8/E_7.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons