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arXiv · 2509.12368

Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems

Evan Sundbo
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Abstract

In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincar\'e polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincar\'e polynomial of any hypertoric Hitchin system, given knowledge of a finite number of base cases.

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Evan Sundbo. 2025-09-15. Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems. https://arxiv.org/abs/2509.12368

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