Double ramification cycles and integrable systems

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3. Compare $\mathrm{DR}_g^\mathrm{adm}(A)$ with $\mathrm{DR}_g^\mathrm{rel}(A)$

General Proposal : Compare

$\mathrm{DR}_g^{\mathrm{adm}}(A)$ with

$\mathrm{DR}_g^{\mathrm{rel}}(A)$ . The latter object has been defined geometrically in different, mostly equivalent ways: Using the Abel-Jacobi map by Holmes, Kass - Pagani, Marcus - Wise, and using relative stable maps by Guéré, Marcus - Wise.

Sub-question: Is the degree

$2d$ part of

$\mathrm{DR}_g^d(A)$ supported on some specific stable graphs (no loops?). -Answer: No, one get contributions from many different graphs

Cite this as: AimPL: Double ramification cycles and integrable systems, available at http://aimpl.org/doubleramific.

Choose a section to move this problem to.

A conjecture of Buryak-Rossi
Meaning of higher $r$ -coefficients in $\mathrm{DR}_g^{d,r}(A)$
Integrable hierarchies from partial CohFTs
Quantization for DR hierarchy
Reconstruction for semisimple F-CohFTs
The Tropical DR cycle
Double double ramification cycles
Universal DR cycles
DR-hierarchy with target
Theta divisors on toroidal compactifications of universal Jacobians
Comparison of GRR formulas and JPPZ formulas for DR cycle
Kontsevich-Witten series with $\hbar$

Double ramification cycles and integrable systems

3. Compare \mathrm{DR}_g^\mathrm{adm}(A)\mathrm{DR}_g^\mathrm{adm}(A) with \mathrm{DR}_g^\mathrm{rel}(A)\mathrm{DR}_g^\mathrm{rel}(A)

3. Compare $\mathrm{DR}_g^\mathrm{adm}(A)$ with $\mathrm{DR}_g^\mathrm{rel}(A)$