Obstruction Theory
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. he older meaning for obstruction theory in homotopy theory relates to a procedure, inductive with respect to dimension, for extending a continuous mapping defined on a simplicial complex, or CW complex. Traditionally called Eilenberg obstruction theory, after Samuel Eilenberg. It involves cohomology groups with coefficients in homoto...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. he older meaning for obstruction theory in homotopy theory relates to a procedure, inductive with respect to dimension, for extending a continuous mapping defined on a simplicial complex, or CW complex. Traditionally called Eilenberg obstruction theory, after Samuel Eilenberg. It involves cohomology groups with coefficients in homotopy groups to define obstructions to extensions. For example, with a mapping from a simplicial complex X to another, Y, defined initially on the 0-skeleton of X (the vertices of X), an extension to the 1-skeleton will be possible whenever Y is sufficiently path-connected. Extending from the 1-skeleton to the 2-skeleton means filling in the images of the solid triangles from X, given the imageof the edges.
