Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Walpuski, Thomas"'
Autor:
Doan, Aleksander, Walpuski, Thomas
Motivated by counting pseudo-holomorphic curves in symplectic Calabi-Yau $3$-folds, this article studies a chamber structure in the space of real Cauchy-Riemann operators on a Riemann surface, and constructs three chambered invariants associated with
Externí odkaz:
http://arxiv.org/abs/2410.21057
This article constructs examples of associative submanifolds in $G_2$-manifolds obtained by resolving $G_2$-orbifolds using Joyce's generalised Kummer construction. As the $G_2$-manifolds approach the $G_2$-orbifolds, the volume of the associative su
Externí odkaz:
http://arxiv.org/abs/2202.00522
The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many vanish in every homology class. The integrality part of this conjectur
Externí odkaz:
http://arxiv.org/abs/2103.08221
Autor:
Doan, Aleksander, Walpuski, Thomas
The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the intersections of concrete families of elliptic operators with these subm
Externí odkaz:
http://arxiv.org/abs/2006.01352
Autor:
Doan, Aleksander, Walpuski, Thomas
Based on computations of Pandharipande, Zinger proved that the Gopakumar-Vafa BPS invariants $\mathrm{BPS}_{A,g}(X,\omega)$ for primitive Calabi-Yau classes and arbitrary Fano classes $A$ on a symplectic $6$-manifold $(X,\omega)$ agree with the signe
Externí odkaz:
http://arxiv.org/abs/1910.12338
Autor:
Walpuski, Thomas, Zhang, Boyu
Publikováno v:
Duke Mathematical Journal 170.17 pp. 3891-3934 (2021)
We prove an abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three. This result recovers Taubes' compactness theorem for stable flat $\mathbf{P}\mathrm{SL}_2(\mathbf{C})$-connections as well as the compac
Externí odkaz:
http://arxiv.org/abs/1904.03749
Autor:
He, Siqi, Walpuski, Thomas
Publikováno v:
Journal of Geometry and Physics 146 (2019)
We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This correspondence was conjectured by Witten and plays an important role in
Externí odkaz:
http://arxiv.org/abs/1812.08994
Autor:
Doan, Aleksander, Walpuski, Thomas
Publikováno v:
Advances in Mathematics 379 (2021)
This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, we establish a new result in this direct
Externí odkaz:
http://arxiv.org/abs/1809.04731
Autor:
Doan, Aleksander, Walpuski, Thomas
Publikováno v:
Pure and Applied Mathematics Quarterly 15.4 (2019) pp. 1047-1133
Building on ideas from [DT98; DS11; Wal17; Hay17], we outline a proposal for constructing Floer homology groups associated with a G2-manifold. These groups are generated by associative submanifolds and solutions of the ADHM Seiberg-Witten equations.
Externí odkaz:
http://arxiv.org/abs/1712.08383
Autor:
Doan, Aleksander, Walpuski, Thomas
Publikováno v:
Journal of Differential Geometry 117.3 (2021) pp. 395-449
We prove the existence of singular harmonic ${\bf Z}_2$ spinors on $3$-manifolds with $b_1 > 1$. The proof relies on a wall-crossing formula for solutions to the Seiberg-Witten equation with two spinors. The existence of singular harmonic ${\bf Z}_2$
Externí odkaz:
http://arxiv.org/abs/1710.06781