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PreprintCC BY-NC-SA 4.0arXiv

Equivariant Milnor map

  • Mathilda Campillo
  • Yuanxin Guan
  • Zhi Lü
  • Bernardo Uribe
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Abstract

The Milnor map is the homomorphism from the unitary bordism ring to the unoriented bordism ring, halving the dimension, that maps the unitary bordism classes of the complex Milnor hypersurfaces to the unoriented bordism classes of their real points. In this work, we propose to generalize this construction to the equivariant setup and we show the existence of such a map for the equivariant unitary groups of the circle and the cyclic group of order two. Furthermore, we relate the kernel of these Milnor maps to the magnetic unitary equivariant bordism groups of free conjugations.

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Cite

BibTeXRIS
BibTeX
@misc{campillo2026equivariant,
  title = {{Equivariant Milnor map}},
  author = {Mathilda Campillo and Yuanxin Guan and Zhi Lü and Bernardo Uribe},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.12697},
  eprint = {2606.12697},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.12697},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Equivariant Milnor map
AU  - Mathilda Campillo
AU  - Yuanxin Guan
AU  - Zhi Lü
AU  - Bernardo Uribe
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2606.12697
UR  - https://arxiv.org/abs/2606.12697
AB  - The Milnor map is the homomorphism from the unitary bordism ring to the unoriented bordism ring, halving the dimension, that maps the unitary bordism classes of the complex Milnor hypersurfaces to the unoriented bordism classes of their real points. In this work, we propose to generalize this construction to the equivariant setup and we show the existence of such a map for the equivariant unitary groups of the circle and the cyclic group of order two. Furthermore, we relate the kernel of these Milnor maps to the magnetic unitary equivariant bordism groups of free conjugations.
ER  -