Genus-zero r-spin theory

Renzo Cavalieri; Tyler Kelly; Rob Silversmith

Genus-zero r-spin theory

Renzo Cavalieri, Tyler Kelly, Rob Silversmith^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

Original language	English
Journal	Moduli
Publication status	Accepted/In press - 20 Nov 2023

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Not yet published as of 22/04/2024.

1 Preprint

Genus-zero r-spin theory
Cavalieri, R., Kelly, T. & Silversmith, R., 29 May 2023, arXiv.
Research output: Working paper/Preprint › Preprint

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title = "Genus-zero r-spin theory",

abstract = "We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.",

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AU - Cavalieri, Renzo

AU - Kelly, Tyler

AU - Silversmith, Rob

N1 - Not yet published as of 22/04/2024.

PY - 2023/11/20

Y1 - 2023/11/20

N2 - We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

AB - We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

UR - https://moduli.nl/openaccess

UR - https://www.cambridge.org/core/journals/moduli

M3 - Article

JO - Moduli

JF - Moduli

ER -

Genus-zero r-spin theory

Abstract

Bibliographical note

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Genus-zero r-spin theory

Cite this