Universität zu Köln

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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Abstract

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
Creators:	Creators Email ORCID ORCID Put Code Godinho, Leonor UNSPECIFIED orcid.org/0000-0002-6329-3002 UNSPECIFIED Pelayo, Alvaro UNSPECIFIED UNSPECIFIED UNSPECIFIED Sabatini, Silvia UNSPECIFIED orcid.org/0000-0001-7521-321X UNSPECIFIED
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
Publisher:	INT PRESS BOSTON, INC
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:	Keywords Language MANIFOLDS Multiple languages Mathematics, Applied; Mathematics; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/41497