Obstruction theory studies the extensibility of maps using algebraic gadgets. While the terminology rapidly becomes technical and convoluted (as Iyanaga and Kawada (1980) 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.
Obstruction
See also
Algebraic Topology, Chern Class, Eilenberg-Mac Lane Space, Stiefel-Whitney ClassExplore with Wolfram|Alpha
References
Iyanaga, S. and Kawada, Y. (Eds.). "Obstructions." §300 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 948-950, 1980.Referenced on Wolfram|Alpha
ObstructionCite this as:
Weisstein, Eric W. "Obstruction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Obstruction.html