[HTML][HTML] On orientations for gauge-theoretic moduli spaces
Let X be a compact manifold, D: Γ∞(E 0)→ Γ∞(E 1) a real elliptic operator on X, G a Lie
group, P→ X a principal G-bundle, and BP the infinite-dimensional moduli space of all …
group, P→ X a principal G-bundle, and BP the infinite-dimensional moduli space of all …
PSL (2; C) connections on 3-manifolds with L2 bounds on curvature
CH Taubes - arXiv preprint arXiv:1205.0514, 2012 - arxiv.org
Karen Uhlenbeck's compactness theorem for sequences of connections with L2 bounds on
curvature applies only to connections on principal bundles with compact structure group …
curvature applies only to connections on principal bundles with compact structure group …
The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
CH Taubes - arXiv preprint arXiv:1407.6206, 2014 - arxiv.org
Supposing that X is a Riemannian manifold, a Z/2 spinor on X is defined by a data set
consisting of a closed set in X to be denoted by Z, a real line bundle over XZ, and a nowhere …
consisting of a closed set in X to be denoted by Z, a real line bundle over XZ, and a nowhere …
Geometric flows from unified string theories
DH Phong - arXiv preprint arXiv:2304.02533, 2023 - arxiv.org
A survey of new geometric flows motivated by string theories is provided. Their settings can
range from complex geometry to almost-complex geometry to symplectic geometry. From the …
range from complex geometry to almost-complex geometry to symplectic geometry. From the …
A family of instanton-invariants for four-manifolds and their relation to Khovanov homology
M Bleher - arXiv preprint arXiv:2412.13285, 2024 - arxiv.org
This article reviews Witten's gauge-theoretic approach to Khovanov homology from the
perspective of Haydys-Witten instanton Floer theory. Expanding on Witten's arguments, we …
perspective of Haydys-Witten instanton Floer theory. Expanding on Witten's arguments, we …
The behavior of sequences of solutions to the Vafa-Witten equations
CH Taubes - arXiv preprint arXiv:1702.04610, 2017 - arxiv.org
The Vafa-Witten equations on an oriented Riemannian 4-manifold are first order, non-linear
equations for a pair of connection on a principle SO (3) bundle over the 4-manifold and a …
equations for a pair of connection on a principle SO (3) bundle over the 4-manifold and a …
Sequences of Nahm pole solutions to the SU (2) Kapustin-Witten equations
CH Taubes - arXiv preprint arXiv:1805.02773, 2018 - arxiv.org
This paper describes the behavior of sequences of solutions to the Kapustin-Witten
equations with Nahm pole asymptotics on the product of the half-line with a compact …
equations with Nahm pole asymptotics on the product of the half-line with a compact …
Geometric analysis of the Yang–Mills connections over compact Kähler surfaces
T Huang - Calculus of Variations and Partial Differential …, 2024 - Springer
In this article, we study the Yang–Mills connection A on a principal G-bundle P over a
compact Kähler surface (X, g) with a generic Kähler metric g. We first construct a gluing …
compact Kähler surface (X, g) with a generic Kähler metric g. We first construct a gluing …
On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces
Y Tanaka - Geometriae Dedicata, 2019 - Springer
This article finds a structure of singular sets on compact Kähler surfaces, which Taubes
introduced in the studies of the asymptotic analysis of solutions to the Kapustin–Witten …
introduced in the studies of the asymptotic analysis of solutions to the Kapustin–Witten …
On the behavior of sequences of solutions to U (1) Seiberg-Witten systems in dimension 4
CH Taubes - arXiv preprint arXiv:1610.07163, 2016 - arxiv.org
This paper studies the behavior of sequences of solutions to Seiberg-Witten like equations
for a pair consisting of a Hermitian connection on a line bundle over a 4-dimensional …
for a pair consisting of a Hermitian connection on a line bundle over a 4-dimensional …