Nathaniel Bottman

activity

20142026

most cited2-associahedra

13 citations · 27 across the 16 of their papers we have counts for

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9 papers · 1 filter

math.SG2024

Adiabatic Fredholm Theory

Nathaniel Bottman, Katrin Wehrheim

We develop a robust functional analytic framework for adiabatic limits. This framework consist of a notion of adiabatic Fredholm family, several possible regularity properties, and…

math.SG2024

Foundations of $(A_{\infty}, 2)$ -categories: from flow to linear

Nathaniel Bottman, Katrin Wehrheim

This paper provides a blueprint for the construction of a symplectic $(A_{\infty}, 2)$ -category, $Symp$ . We develop two ways of encoding the information in $Symp$ --…

math.SG2024

The focus-focus addition graph is immersed

Mohammed Abouzaid, Nathaniel Bottman, Yunpeng Niu

For a symplectic 4-manifold $M$ equipped with a singular Lagrangian fibration with a section, the natural fiberwise addition given by the local Hamiltonian flow is well-defined on…

math.SG2022

Functoriality in categorical symplectic geometry

Mohammed Abouzaid, Nathaniel Bottman

Categorical symplectic geometry is the study of a rich collection of invariants of symplectic manifolds, including the Fukaya $A_{\infty}$ -category, Floer cohomology, and symplectic…

math.SG2018

Explicit constructions of quilts with seam condition coming from symplectic reduction

Nathaniel Bottman

Associated to a symplectic quotient $M / / G$ is a Lagrangian correspondence $Λ_{G}$ from $M / / G$ to $M$ . In this note, we construct in two examples quilts with seam condition on suc…

math.SG2017

Moduli spaces of witch curves topologically realize the 2-associahedra

Nathaniel Bottman

For $r \geq 1$ and $n \in Z_{\geq 0}^{r} ∖ {0}$ , we construct the compactified moduli space $2 M_{n}$ of witch curves o…

math.SG2017★ 13 cited

2-associahedra

Nathaniel Bottman

For any $r \geq 1$ and $n \in Z_{\geq 0}^{r} ∖ {0}$ we construct a poset $W_{n}$ called a 2-associahedron. The 2-associahedra arose in sympl…

math.SG2015

Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts

Nathaniel Bottman, Katrin Wehrheim

We establish a Gromov compactness theorem for strip shrinking in pseudoholomorphic quilts when composition of Lagrangian correspondences is immersed. In particular, we show that fi…

math.SG2014

Pseudoholomorphic quilts with figure eight singularity

Nathaniel Bottman

We show that the novel figure eight singularity in a pseudoholomorphic quilt can be continuously removed when composition of Lagrangian correspondences is cleanly immersed. The pro…

Adiabatic Fredholm Theory

Foundations of (A∞​,2)-categories: from flow to linear

The focus-focus addition graph is immersed

Functoriality in categorical symplectic geometry

Explicit constructions of quilts with seam condition coming from symplectic reduction

Moduli spaces of witch curves topologically realize the 2-associahedra

2-associahedra

Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts

Pseudoholomorphic quilts with figure eight singularity

Foundations of $(A_{\infty}, 2)$ -categories: from flow to linear