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Multi-monopoles and monodromy around the wobbly divisor

  • Brad Wilson
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Abstract

The multi-monopole equations are a generalisation of the Seiberg--Witten equations where the spinor is coupled to an auxiliary vector bundle. The signed count of multi-monopoles on a 3-manifold can vary according to a new type of wall-crossing phenomenon. For products S1× C, where C is a closed Riemann surface, we relate the wall and chamber structure to loops in the complement of the wobbly divisor of C. Such a loop induces a monodromy map on the multi-vortex moduli space, and the count of its fixed points is expected to agree with the count of multi-monopoles on S1× C in the given chamber. By studying singularities of framed multi-vortex moduli spaces, we are able to understand these monodromy maps for various loops. Counting fixed points suggests that product 3-manifolds display incredibly rich wall-crossing behaviour.

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Cite

BibTeXRIS
BibTeX
@misc{wilson2026multimonopoles,
  title = {{Multi-monopoles and monodromy around the wobbly divisor}},
  author = {Brad Wilson},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08760},
  eprint = {2611.08760},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08760},
}
RIS
TY  - UNPB
TI  - Multi-monopoles and monodromy around the wobbly divisor
AU  - Brad Wilson
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08760
UR  - https://arxiv.org/abs/2611.08760
AB  - The multi-monopole equations are a generalisation of the Seiberg--Witten equations where the spinor is coupled to an auxiliary vector bundle. The signed count of multi-monopoles on a 3-manifold can vary according to a new type of wall-crossing phenomenon. For products S^1× C, where C is a closed Riemann surface, we relate the wall and chamber structure to loops in the complement of the wobbly divisor of C. Such a loop induces a monodromy map on the multi-vortex moduli space, and the count of its fixed points is expected to agree with the count of multi-monopoles on S^1× C in the given chamber. By studying singularities of framed multi-vortex moduli spaces, we are able to understand these monodromy maps for various loops. Counting fixed points suggests that product 3-manifolds display incredibly rich wall-crossing behaviour.
ER  -