Niemeier lattices, smooth 4-manifolds and instantons

Research output: Contribution to journalArticlepeer-review


We show that the set of even positive definite lattices that arise from smooth, simply-connected 4-manifolds bounded by a fixed homology 3-sphere can depend on more than the ranks of the lattices. We provide two homology 3-spheres with distinct sets of such lattices, each containing a distinct nonempty subset of the rank 24 Niemeier lattices.

Original languageEnglish (US)
Pages (from-to)549-568
Number of pages20
JournalMathematische Annalen
Issue number1-2
StatePublished - Feb 2021
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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