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One of the most important problems of topology (and [[algebraic topology]] in particular) is the precise and rigorous characterization of the "holes" in a space.  This characterization is in terms of some [[group|groups]] known as the homotopy groups and homology groups.  The most important of these is the 1st homotopy group, known as the '''fundamental group'''.

One of the most important problems of topology (and [[algebraic topology]] in particular) is the precise and rigorous characterization of the "holes" in a space.  This characterization is in terms of some [[group|groups]] known as the homotopy groups and homology groups.  The most important of these is the 1st homotopy group, known as the '''fundamental group'''.