Loading...
Please wait, while we are loading the content...
Similar Documents
FERMAT AND THE NUMBER OF FIXED POINTS OF PERIODIC FLOWS
| Content Provider | Semantic Scholar |
|---|---|
| Author | Godinho, Leonor Pelayo, Álvaro Sabatini, Silvia |
| Copyright Year | 2014 |
| Abstract | We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold M of dimension 2n with nonempty fixed point set, provided the Chern number c1cn−1[M ] vanishes. The proof combines techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, introduced by Pierre de Fermat. This lower bound confirms in many cases a conjecture of Kosniowski from 1979, and is better than existing bounds for some symplectic actions. Moreover, if the fixed point set is discrete, we 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.ucsd.edu/~alpelayo/Docs/fermat.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Fermat Fixed point (mathematics) Fixed-Point Number Hamiltonian (quantum mechanics) Symplectic integrator Torsion (gastropod) YAU 17, (trans)-isomer manifold |
| Content Type | Text |
| Resource Type | Article |
