Godinho, Leonor ORCID: 0000-0002-6329-3002, Pelayo, Alvaro and Sabatini, Silvia ORCID: 0000-0001-7521-321X (2015). Fermat and the number of fixed points of periodic flows. Commun. Number Theory Phys., 9 (4). S. 643 - 688. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1931-4531

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We compute explicit lower bounds for the number of fixed points of a circle action on a compact almost complex manifold M-2n with nonempty fixed point set, provided the Chern number c(1)c(n-1)[M] vanishes. The proofs combine techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, stated by Fermat. These lower bounds depend only on n and, in some cases, are better than existing bounds. If the fixed point set is discrete, we also prove divisibility properties for the number of fixed points, improving similar statements obtained by Hirzebruch in 1999. Our results apply, for example, to a class of manifolds which do not support any Hamiltonian circle action, namely those for which the first Chern class is torsion. This includes, for instance, all symplectic Calabi Yau manifolds.

Item Type: Journal Article
CreatorsEmailORCIDORCID Put Code
Godinho, LeonorUNSPECIFIEDorcid.org/0000-0002-6329-3002UNSPECIFIED
Sabatini, SilviaUNSPECIFIEDorcid.org/0000-0001-7521-321XUNSPECIFIED
URN: urn:nbn:de:hbz:38-414979
DOI: 10.4310/CNTP.2015.v9.n4.a1
Journal or Publication Title: Commun. Number Theory Phys.
Volume: 9
Number: 4
Page Range: S. 643 - 688
Date: 2015
Place of Publication: SOMERVILLE
ISSN: 1931-4531
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects: no entry
Uncontrolled Keywords:
MANIFOLDSMultiple languages
Mathematics, Applied; Mathematics; Physics, MathematicalMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/41497


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