# fundamental group

fundamental group
The group whose elements are homotopy classes of images of the closed interval in a specified topological space, such that the endpoints are both mapped to a designated point, and whose operation is concatenation.

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• Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

• fundamental group — noun Date: 1957 a set that is a subset of all paths defined on a set of points each pair of which is joined by a path and that is the quotient group of the group of all paths beginning and ending in a given point …   New Collegiate Dictionary

• fundamental group — noun : a set that is a subset of all paths defined on a set of points each pair of which is joined by a path and that is the quotient group of the group of all paths beginning and ending in the given point …   Useful english dictionary

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• Group extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… …   Wikipedia