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Peer-reviewedCC BYJournal of the European Mathematical Society

Lattice homology and Seiberg–Witten Floer spectra

  • Irving Dai1
  • Hirofumi Sasahira2
  • Matthew Stoffregen3
  1. 1The University of Texas at Austin, USA
  2. 2Kyushu University, Fukuoka, Japan
  3. 3Michigan State University, East Lansing, USA
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Abstract

Using lattice homology, we give an explicit combinatorial description of the Seiberg–Witten Floer spectrum \mathit{SWF}(Y) for Y an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational homology spheres with base orbifold S^{2} . Using our computations, we provide a calculation of Manolescu’s \kappa -invariant for certain connected sums of these spaces.

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Cite

BibTeXRIS
BibTeX
@article{dai2026lattice,
  title = {{Lattice homology and Seiberg–Witten Floer spectra}},
  author = {Irving Dai and Hirofumi Sasahira and Matthew Stoffregen},
  journal = {Journal of the European Mathematical Society},
  year = {2026},
  month = jul,
  doi = {10.4171/jems/1809},
  url = {https://doi.org/10.4171/jems/1809},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Lattice homology and Seiberg–Witten Floer spectra
AU  - Irving Dai
AU  - Hirofumi Sasahira
AU  - Matthew Stoffregen
PY  - 2026
DA  - 2026/07/31
JO  - Journal of the European Mathematical Society
DO  - 10.4171/jems/1809
UR  - https://doi.org/10.4171/jems/1809
AB  - Using lattice homology, we give an explicit combinatorial description of the Seiberg–Witten Floer spectrum \mathit{SWF}(Y) for Y an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational homology spheres with base orbifold S^{2} . Using our computations, we provide a calculation of Manolescu’s \kappa -invariant for certain connected sums of these spaces.
SN  - 1435-9855
SN  - 1435-9863
ER  -