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The cohomology of projective unitary groups

Haibao Duan

Abstract

The projective unitary group PU(n) is the quotient of the unitary group U(n) by its center. We compute the integral cohomology ring of PU(n) using explicit constructed generators.

The cohomology of projective unitary groups

Abstract

The projective unitary group PU(n) is the quotient of the unitary group U(n) by its center. We compute the integral cohomology ring of PU(n) using explicit constructed generators.

Paper Structure

This paper contains 9 sections.

Table of Contents

  1. Introduction
  2. The binomial coefficients $\binom{n}{r}$
  3. Spectral sequence of the fibration $\pi :$ $G\rightarrow G/T$
  4. The complex $\{E_{2}^{\ast ,\ast }(G),d_{2}\}$ for $G=U(n)$ or $PU(n)$
  5. The map $\pi ^{\ast }:E_{3}^{\ast ,0}(G)\rightarrow H^{\ast }(G)$
  6. The map $\kappa :E_{3}^{\ast ,1}(G)\rightarrow H^{\ast }(G)$
  7. A refinement of the Gysin sequence (1.3)
  8. Proofs of Theorem A and B
  9. Main result and examples