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45![Homotopy theory begins with the homotopy groups πn (X) , which are the natural higher-dimensional analogs of the fundamental group. These higher homotopy groups have certain formal similarities with homology groups. For example, πn (X) turns out to be always abelian for n ≥ 2 , and there are relative homotopy groups fitting into a long exact sequence just like the long exact sequence of homology groups. Homotopy theory begins with the homotopy groups πn (X) , which are the natural higher-dimensional analogs of the fundamental group. These higher homotopy groups have certain formal similarities with homology groups. For example, πn (X) turns out to be always abelian for n ≥ 2 , and there are relative homotopy groups fitting into a long exact sequence just like the long exact sequence of homology groups.](https://www.pdfsearch.io/img/6b20123cd362db93175874009f9c2c9b.jpg) | Add to Reading ListSource URL: www.math.cornell.eduLanguage: English - Date: 2013-06-04 09:21:10
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49![VOL. 28, 1942 MA THEMA TICS: EILENBERG AND MacLANE VOL. 28, 1942 MA THEMA TICS: EILENBERG AND MacLANE](https://www.pdfsearch.io/img/0a6de8156e386a084dd0659821d8d435.jpg) | Add to Reading ListSource URL: www.ncbi.nlm.nih.govLanguage: English |
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