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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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Abstract

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
Additional Information:

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
MIMS number:2008.54
Deposited By:Dr Theodore Voronov
Deposited On:05 May 2008

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