Gregory J. Parker

activity

20222026

collaborators

7 papers

math.DG2026

Nonproduct Minimal Submanifolds with Cylindrical Tangent Cones

Rafe Mazzeo, Gregory J. Parker

This article constructs, via perturbation methods, infinite-dimensional families of non-product minimal submanifolds which have singular sets locally modeled on cylindrical tangent…

math.DG2026

The universal moduli space of non-degenerate $Z /2 Z$ harmonic spinors

Siqi He, Gregory J. Parker, Thomas Walpuski

This article equips the universal moduli spaces of non-degenerate $Z /2 Z$ harmonic spinors and eigenspinors with tame Fréchet manifold structures and proves that t…

math.DG2024

$Z_{2}$ -Harmonic Spinors and 1-forms on Connected sums and Torus sums of 3-manifolds

Siqi He, Gregory J. Parker

Given a pair of $Z_{2}$ -harmonic spinors (resp. 1-forms) on closed Riemannian 3-manifolds $(Y_{1}, g_{1})$ and $(Y_{2}, g_{2})$ , we construct $Z_{2}$ -harmonic spinors (resp. 1…

math.DG2024

Gluing $Z_{2}$ -Harmonic Spinors and Seiberg-Witten Monopoles on 3-Manifolds

Gregory J. Parker

Given a $Z_{2}$ -harmonic spinor satisfying some genericity assumptions, this article constructs a 1-parameter family of two-spinor Seiberg-Witten monopoles converging to it a…

math.DG2023

Concentrating Dirac Operators and Generalized Seiberg-Witten Equations

Gregory J. Parker

This article studies a class of Dirac operators of the form $D_{ε} = D + ε^{- 1} A$ , where $A$ is a zeroth order perturbation vanishing on a subbundl…

math.DG2023

Deformations of $Z_{2}$ -Harmonic Spinors on 3-Manifolds

Gregory J. Parker

A $Z_{2}$ -harmonic spinor on a 3-manifold $Y$ is a solution of the Dirac equation on a bundle that is twisted around a submanifold $Z$ of codimension 2 called the si…

math.DG2022

Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations on 3-Manifolds

Gregory J. Parker

Given a compact 3-manifold $Y$ and a $Z_{2}$ -harmonic spinor $(Z_{0}, A_{0}, Φ_{0})$ with singular set $Z_{0}$ , this article constructs a family of local solutions t…

Nonproduct Minimal Submanifolds with Cylindrical Tangent Cones

The universal moduli space of non-degenerate Z/2Z harmonic spinors

Z2​-Harmonic Spinors and 1-forms on Connected sums and Torus sums of 3-manifolds

Gluing Z2​-Harmonic Spinors and Seiberg-Witten Monopoles on 3-Manifolds

Concentrating Dirac Operators and Generalized Seiberg-Witten Equations

Deformations of Z2​-Harmonic Spinors on 3-Manifolds

Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations on 3-Manifolds

The universal moduli space of non-degenerate $Z /2 Z$ harmonic spinors

$Z_{2}$ -Harmonic Spinors and 1-forms on Connected sums and Torus sums of 3-manifolds

Gluing $Z_{2}$ -Harmonic Spinors and Seiberg-Witten Monopoles on 3-Manifolds

Deformations of $Z_{2}$ -Harmonic Spinors on 3-Manifolds