topological_recursion

topological_recursion#

Topological recursion

This module implements topological recursion. In particular it makes available the computation of various integral of cohomology classes on M_{g,n} (psi, lambda and kappa classes).

REFS:

  • G. Borot “Topological recursion and geometry” arXiv:1705.09986

  • J. E. Andersen, G. Borot, L. O. Chekhov, N. Orantin “The ABCD of topological recursion” arXiv:1703.03307

  • R. Pandharipande “Cohomological field theory calculations” arXiv:1712.02528

TODO:

  • generic symbolic TR

  • other recursions: - ELSV, Eynard Bouchard-Marino conjectures and simple Hurwitz numbers (lambda classes) - bundle of quadratic differentials and co

  • generating series

  • simplification of the recursion via the generalized string and dilaton

class surface_dynamics.topological_recursion.topological_recursion.TopologicalRecursion(cache_all=False, base_ring=None)#

A generic topological recursion.

For concrete examples see:

A(i, j, k)#
B(g, n, i, j)#
C(g, n, i)#
D(i)#
F(g, n, I)#

Return the value of the partition function F_{g,n}(I) where I = (i_0, i_1, …, i_{n-1}) is a tuple of n non-negative integers whose sum is <= 3g-3+n.

We assume here that the topological recursion given by A, B, C and D produces a partition function symmetric in the variables i_0, i_1, …, i_{n-1}.

polynomial(g, n, ring=None)#
write(g, n, s=None)#

Print normalized values of the polynomials F_{g,n}

surface_dynamics.topological_recursion.topological_recursion.compositions(g, n)#

Return compositions of sum at most 3g-3+n and length n

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