2008.54: Combinatorics of simple polytopes and differential equations
2008.54: Victor M. Buchstaber (2008) Combinatorics of simple polytopes and differential equations.
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Simple polytopes play important role in applications of algebraic geometry to physics. They are also main objects in toric topology.
There is a commutative associative ring P generated by simple polytopes. The ring P possesses a natural derivation d, which comes from the boundary operator. We shall describe a ring homomorphism from the ring P to the ring of polynomials Z[t,α] transforming the operator d to the partial derivative ∂/∂t.
This result opens way to a relation between polytopes and differential equations. As it has turned out, certain important series of polytopes (including some recently discovered) lead to fundamental nonlinear differential equations in partial derivatives
|Item Type:||MIMS Preprint|
Talk at the Manchester Geometry Seminar on Thursday 21 February 2008
|Uncontrolled Keywords:||Simple polytopes, simple polyhedra, Stasheff polyhedra, differential equations, Bott-Taubes polytopes, Hopf equation, complex cobordism|
|Subjects:||MSC 2000 > 05 Combinatorics|
MSC 2000 > 33 Special functions (properties of functions as functions)
MSC 2000 > 55 Algebraic topology
|Deposited By:||Dr Theodore Voronov|
|Deposited On:||05 May 2008|