Obstruction theory studies the extentability of Maps using algebraic Gadgets. While the terminology rapidly becomes technical and convoluted (as Iyanaga and Kawada note, ``It is extremely difficult to discuss higher obstructions in general since they involve many complexities''), the ideas associated with obstructions are very important in modern Algebraic Topology.

**References**

Iyanaga, S. and Kawada, Y. (Eds.). ``Obstructions.'' §300 in
*Encyclopedic Dictionary of Mathematics.* Cambridge, MA: MIT Press, pp. 948-950, 1980.

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1999-05-26