On the compactness problem for a family of generalized seiberg–witten equations in dimension 3

Thomas Walpuski; Boyu Zhang

doi:10.1215/00127094-2021-0005

On the compactness problem for a family of generalized seiberg–witten equations in dimension 3

Thomas Walpuski
, Boyu Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove an abstract compactness theorem for a family of generalized Seiberg–Witten equations in dimension 3. This result recovers Taubes’s compactness theorem for stable flat PSL₂.C/-connections as well as the compactness theorem for Seiberg–Witten equations with multiple spinors by Haydys and Walpuski. Furthermore, this result implies a compactness theorem for the ADHM_1;2 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.

Original language	English (US)
Pages (from-to)	3891-3934
Number of pages	44
Journal	Duke Mathematical Journal
Volume	170
Issue number	17
DOIs	https://doi.org/10.1215/00127094-2021-0005
State	Published - Nov 15 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-2021-0005

Cite this

@article{5e9716198eb647ba989108712e0d3d2c,

title = "On the compactness problem for a family of generalized seiberg–witten equations in dimension 3",

abstract = "We prove an abstract compactness theorem for a family of generalized Seiberg–Witten equations in dimension 3. This result recovers Taubes{\textquoteright}s compactness theorem for stable flat PSL2.C/-connections as well as the compactness theorem for Seiberg–Witten equations with multiple spinors by Haydys and Walpuski. Furthermore, this result implies a compactness theorem for the ADHM1;2 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.",

author = "Thomas Walpuski and Boyu Zhang",

note = "Publisher Copyright: {\textcopyright} 2021",

year = "2021",

month = nov,

day = "15",

doi = "10.1215/00127094-2021-0005",

language = "English (US)",

volume = "170",

pages = "3891--3934",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "17",

}

TY - JOUR

T1 - On the compactness problem for a family of generalized seiberg–witten equations in dimension 3

AU - Walpuski, Thomas

AU - Zhang, Boyu

PY - 2021/11/15

Y1 - 2021/11/15

N2 - We prove an abstract compactness theorem for a family of generalized Seiberg–Witten equations in dimension 3. This result recovers Taubes’s compactness theorem for stable flat PSL2.C/-connections as well as the compactness theorem for Seiberg–Witten equations with multiple spinors by Haydys and Walpuski. Furthermore, this result implies a compactness theorem for the ADHM1;2 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.

AB - We prove an abstract compactness theorem for a family of generalized Seiberg–Witten equations in dimension 3. This result recovers Taubes’s compactness theorem for stable flat PSL2.C/-connections as well as the compactness theorem for Seiberg–Witten equations with multiple spinors by Haydys and Walpuski. Furthermore, this result implies a compactness theorem for the ADHM1;2 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.

UR - https://www.scopus.com/pages/publications/85120817389

UR - https://www.scopus.com/pages/publications/85120817389#tab=citedBy

U2 - 10.1215/00127094-2021-0005

DO - 10.1215/00127094-2021-0005

M3 - Article

AN - SCOPUS:85120817389

SN - 0012-7094

VL - 170

SP - 3891

EP - 3934

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 17

ER -

On the compactness problem for a family of generalized seiberg–witten equations in dimension 3

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this