HAMILTONIAN CIRCLE ACTIONS ON EIGHT-DIMENSIONAL MANIFOLDS WITH MINIMAL FIXED SETS

Let the circle act in a Hamiltonian fashion on a closed 8-dimensional sym-plectic manifold M with exactly five fixed points, which is the smallest possible fixed set. In [GS], L. Godinho and S . Sabatini show that if M satisfies an extra “positivity condition” then the isotropy weights at the fixed...

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Bibliographic Details
Published inTransformation groups Vol. 22; no. 2; pp. 353 - 359
Main Authors JANG, D., TOLMAN, S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2017
Springer Nature B.V
Subjects
Algebra
Isotropy
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
Equivariant Cohomology
Complex Manifold
Chern Class
Closed Symplectic Manifold
Cohomology Ring
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Summary:Let the circle act in a Hamiltonian fashion on a closed 8-dimensional sym-plectic manifold M with exactly five fixed points, which is the smallest possible fixed set. In [GS], L. Godinho and S . Sabatini show that if M satisfies an extra “positivity condition” then the isotropy weights at the fixed points of M agree with those of some linear action on ℂℙ 4 . As a consequence, H * ( M ; ℤ) = ℤ[ y ]/ y 5 and c ( TM ) = (1 + y ) 5 . In this paper, we prove that their positivity condition holds for M . This completes the proof of the “symplectic Petrie conjecture” for Hamiltonian circle actions on 8-dimensional closed symplectic manifolds with minimal fixed sets.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-016-9370-0