 Abstract : By extracting the idea and techniques of classical cluster algebras, we construct a class of algebras, named as bistellar cluster algebras from closed oriented triangulated even-dimensional manifolds by performing middle-dimensional bistellar moves. This class of algebras exhibit the algebraic behaviour of middle-dimensional bistellar moves, so the construction of a bistellar cluster algebras has a quite difference from one of a classical cluster algebra. In principle, our construction method for bistellar cluster algebras can also be carried on the more general setting of closed oriented triangulated manifolds of any dimension n (not necessarily is even) by performing various bistellar moves. Moreover, we will use bistellar cluster algebras to construct PL invariants for PL manifolds. This is a joint work with Alastair Darby. |
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