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Then one says that B is a classifying space (K pi, 1)) for the group (pi = pi _1(B )).
a completely general construction of a CW complex which is a classifying space ( B Gamma ) for a finitely presented group (Gamma ), a completely algebraic definition of group cohomology.
(pi _1(S) cong Gamma ), where (Gamma ) is as above, the classifying map (f : S rightarrow X), where X is the Bagnera De Franchis threefold which is a classifying space for (Gamma ), has the property that ( f_* [S] : = Y) satisfies ( Y^3=6).
A Sicilian surface S with (q=p_g=1) is characterized by the following properties: (1) (K_S^2 = 6) (2) ( chi (S) = 1) (3) (pi _1(S) cong Gamma ), where (Gamma ) is as above, (4) the classifying map (f : S rightarrow X), where X is the Bagnera De Franchis threefold which is a classifying space for (Gamma ), has the property that ( f_* [S] : = Y) satisfies ( Y^3=6).
Hence X is a classifying space for the group (Gamma cong pi _1(X)).
Since (C') is a classifying space for the group (pi _{g'}), we obtain a continuous map begin{aligned} m : C' rightarrow BG, pi _1(m) = mu.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com