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Cycles, cocycles, and duality on tropical manifolds


Authors: Andreas Gross and Farbod Shokrieh
Journal: Proc. Amer. Math. Soc. 149 (2021), 2429-2444
MSC (2020): Primary 14T10, 14C17, 05B35, 52B99
DOI: https://doi.org/10.1090/proc/15468
Published electronically: March 26, 2021
MathSciNet review: 4246795
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Abstract: We prove a Poincaré duality for the Chow rings of smooth fans whose support are tropical linear spaces. As a consequence, we show that cycles and cocycles on tropical manifolds are Poincaré dual to each other. This allows us to define pull-backs of tropical cycles along arbitrary morphisms with smooth target.


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Additional Information

Andreas Gross
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
MR Author ID: 1105426
Email: andreas.gross@colostate.edu

Farbod Shokrieh
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
MR Author ID: 917599
ORCID: 0000-0002-6815-3420
Email: farbod@uw.edu

Received by editor(s): September 11, 2020
Received by editor(s) in revised form: December 8, 2020
Published electronically: March 26, 2021
Communicated by: Rachel Pries
Article copyright: © Copyright 2021 American Mathematical Society