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. - Eilenberg - Document - PDFSEARCH.IO

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	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. Add to Reading List Document Date: 2013-06-04 09:21:10 Open Document File Size: 1,26 MB Share Result on Facebook Company Hn / / IndustryTerm cup products / fundamental / nonzero homology / homotopy groups / / Product Freudenthal suspension / / SocialTag Algebraic topology Homotopy group Homotopy Fundamental group Eilenberg–MacLane space CW complex H-space Contractible space Path Topology