Beyond cohomological assignments

Victor Guillemin, Susan Tolman, Catalin Zara

Research output: Contribution to journalArticlepeer-review


Let a torus T act in a Hamiltonian fashion on a compact symplectic manifold (M,ω). The assignment ring AT(M) is an extension of the equivariant cohomology ring HT(M); it is modeled on the GKM description of the equivariant cohomology of a GKM space. We show that AT(M) is a finitely generated S(t)-module, and give a criterion guaranteeing that a given set of assignments generates (alternatively, is a basis for) this module. We define two new types of assignments, delta classes and bridge classes, and show that if the torus T is 2-dimensional, then all assignments of sufficiently high degree are generated by cohomological, delta, and bridge classes. In particular, if M is 6-dimensional, then we can find a basis of such classes.

Original languageEnglish (US)
Article number106976
JournalAdvances in Mathematics
StatePublished - Mar 25 2020


  • Assignments
  • Equivariant cohomology
  • Hamiltonian action

ASJC Scopus subject areas

  • General Mathematics


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