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Geometric recursion. (arXiv:1711.04729v1 [math.GT] CROSS LISTED)
来源于:arXiv
We propose a general theory whose main component are functorial assignments
$$\mathbf{\Sigma} \mapsto \Omega_{\mathbf{\Sigma}} \in
\mathbf{E}(\mathbf{\Sigma}),$$ for a large class of functors $\mathbf{E}$ from
a certain category of bordered surfaces (${\mathbf \Sigma}$'s) to a suitable a
target category of topological vector spaces. The construction is done by
summing appropriate compositions of the initial data over all homotopy classes
of successive excisions of embedded pair of pants. We provide sufficient
conditions to guarantee these infinite sums converge and as a result, we can
generate mapping class group invariant vectors $\Omega_{\mathbf \Sigma}$ which
we call amplitudes. The initial data encode the amplitude for pair of pants and
tori with one boundary, as well as the "recursion kernels" used for glueing. We
give this construction the name of "geometric recursion", abbreviated GR. As an
illustration, we show how to apply our formalism to various spaces of
continuous function 查看全文>>