Some memos on Stable Symplectic Structured Space

Eita Haibara; Shelly Miyano

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arXiv · 2504.09968

Some memos on Stable Symplectic Structured Space

Eita Haibara·Shelly Miyano

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Abstract

In these memos, we define a pregeometry $\mathcal{T}_{\mathbb{S}} ^{alg}$ and a geometry $\mathcal{G}_{\mathbb{S}} ^{alg}$ which integrate symplectic manifolds with $E_{\infty}$-ring sheaves, enabling the construction of $\mathcal{G}_{\mathbb{S}} ^{alg}$-schemes as structured $\infty$-topoi. Our framework and results establish a profound connection between algebraic invariants and homological properties, opening new pathways for exploring symplectic phenomena through the lens of higher category theory and derived geometry.

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Eita Haibara, Shelly Miyano. 2025-04-14. Some memos on Stable Symplectic Structured Space. https://arxiv.org/abs/2504.09968

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