Surfaces and the second homology of a group |
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Authors: | Bruno Zimmermann |
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Institution: | (1) Dipartimento di scienze matematiche, Università degli studi di Trieste, 34100 Trieste, Italy |
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Abstract: | LetG be a group andK(G, 1) an Eilenberg—MacLane space, i.e. 1(K(G,1)) G,
i
(K(G,1))=0,i 1. We give a purely algebraic proof that the second homology groupH
2(G)=H
2(G, ) H
2(K(G,1)) is isomorphic to the group of stable equivalence classes of continuous mapsF K(G,1) inducing surjections on fundamental groups (resp. surjections, whereF {F
g=closed orientable surface of genusg,g![isin](/content/v35gu683543n1h6p/xxlarge8712.gif) }. As a corollary we obtain an algebraic proof of the well-known isomorphismH
2(G)![cong](/content/v35gu683543n1h6p/xxlarge8773.gif) 2(K(G,1)) (2-dimensional bordism group). |
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Keywords: | |
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