Classifying space for SU(n)

In mathematics, the classifying space BSU ⁡ ( n ) {\displaystyle \operatorname {BSU} (n)} for the special unitary group SU ⁡ ( n ) {\displaystyle \operatorname {SU} (n)} is the base space of the universal SU ⁡ ( n ) {\displaystyle \operatorname {SU} (n)} principal bundle ESU ⁡ ( n ) → BSU ⁡ ( n ) {\displaystyle \operatorname {ESU} (n)\rightarrow \operatorname {BSU} (n)} . This means that SU ⁡ ( n ) {\displaystyle \operatorname {SU} (n)} principal bundles over a CW complex up to isomorphism are in bijection with homotopy classes of its continuous maps into BSU ⁡ ( n ) {\displaystyle \operatorname {BSU} (n)} .

Source: Wikipedia — Classifying space for SU(n) (CC BY-SA 4.0)