Third homology of perfect central extensions

B. Mirzaii, F. Y. Mokari, D. C. Ordinola

For a central perfect extension of groups A ↣ G ↠ Q, first we study the natural image of H3(A,Z) in H3(G, Z). As a particular case, we show that if the extension is universal this image is 2-torsion. Moreover when the plus-construction of the classifying space of Q is an H-space, we also study the kernel of the surjective homomorphism H3(G,Z) → H3(Q, Z). 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 14(4) (2021), pp. 61-80