Work

The Cohomology of Projective Unitary Groups

Year: 2024

Type: article

Abstract: The projective unitary group $$\mathrm{PU}(n)$$ is the quotient of the unitary group $$\mathrm{U}(n)$$ by its center $$S^1=\{e^{i\theta}I_n \colon\, \theta\in [0,2\pi]\}$$ , where $$I_n$$ is the identity matrix. Combining the Serre spectral sequence of the fibration $$\mathrm{PU}(n)\to \mathrm{PU}(n)/T$$ with the Gysin sequence of the circle bundle $$\mathrm{U}(n)\to \mathrm{PU}(n)$$ , we compute the integral cohomology ring of $$\mathrm{PU}(n)$$ using explicitly constructed generators, where $$T$$ is a maximal torus of $$\mathrm{PU}(n)$$ .

Source: Proceedings of the Steklov Institute of Mathematics

DOI: 10.1134/s0081543824040084

Author: Haibao Duan

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Tsinghua University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G5331045090