Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation and HNN extension, via the notion of the fundamental group of a graph of groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory.
Read more about Bass–Serre Theory: History, Bass–Serre Covering Trees, Fundamental Theorem of Bass–Serre Theory, Basic Facts and Properties, Trivial and Nontrivial Actions, Hyperbolic Length Functions, Important Developments in Bass–Serre Theory, Generalizations, See Also
Famous quotes containing the word theory:
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)