On Symplectic Invariants Associated to Zoll Manifolds

LDR 02077nam a22003133u 4500
001 100664364
003 MiAaHDL
005 20231111000000.0
006 m d
007 cr bn ---auaua
007 cr||n|||||||||
008 090618s2014 miu sb 000 0 eng d
035 ⊔ ⊔ ‡a(MiU)990135796870106381
035 ⊔ ⊔ ‡asdr-miu.990135796870106381
035 ⊔ ⊔ ‡z(MiU)MIU01000000000000013579687-goog
035 ⊔ ⊔ ‡a(DBlue)diss 108954
035 ⊔ ⊔ ‡z(MiU)Aleph013579687
040 ⊔ ⊔ ‡aMiU ‡cMiU
042 ⊔ ⊔ ‡adc
100 1 ⊔ ‡aHoai, Bich Thuan Vong.
245 1 0 ‡aOn Symplectic Invariants Associated to Zoll Manifolds ‡h[electronic resource].
260 ⊔ ⊔ ‡c2014.
502 ⊔ ⊔ ‡aDissertation (Ph.D.)--University of Michigan. PhD
504 ⊔ ⊔ ‡aIncludes bibliographical references.
520 3 ⊔ ‡amain tools we use are arguments in symplectic geometry and Morse(-Bott) theory. In low dimensions, we make use of a result due to McDuff and Lalonde to classify the 4-dimensional polarized symplectic manifolds up to symplectomorphism.
520 3 ⊔ ‡aIn this thesis, we provide a partial classification for M. Audin’s polarized symplectic manifolds, which are smooth symplectic manifolds endowed with a Morse-Bott function having only two critical values—a minimum, which is attained on a Lagrangian submanifold, and a maximum, which is attained on a symplectic submanifold of codimension 2. We provide examples via Lerman’s symplectic cut construction in which the Lagrangian minima are the Zoll manifolds, i.e. Riemannian manifolds all of whose geodesics are simply closed and of the same period. Given a polarized symplectic manifold with some additional assumptions on the Morse-Bott function, we prove that the Lagrangian minimum must be Zoll and obtain a local equivalence of such manifolds on a neighborhood of the Lagrangian. We then extend the equivalence out towards the symplectic maximum using gradient flows. The
538 ⊔ ⊔ ‡aMode of access: Internet.
650 ⊔ 4 ‡aZoll Manifolds.
650 ⊔ 4 ‡aPolarized Symplectic Manifolds.
690 ⊔ 4 ‡aMathematics.
710 2 ⊔ ‡aUniversity of Michigan. ‡bLibrary. ‡bDeep Blue.
899 ⊔ ⊔ ‡a39015089706546
CID ⊔ ⊔ ‡a100664364
DAT 0 ⊔ ‡a20231111015851.0 ‡b20231111000000.0
DAT 1 ⊔ ‡a20231112060855.0 ‡b2023-11-12T14:53:17Z
DAT 2 ⊔ ‡a2019-11-08T19:00:03Z ‡b2015-09-10T20:00:03Z
CAT ⊔ ⊔ ‡aSDR-MIU ‡cmiu ‡dALMA ‡lprepare.pl-004-008
FMT ⊔ ⊔ ‡aBK
HOL ⊔ ⊔ ‡0sdr-miu.990135796870106381 ‡aMiU ‡bSDR ‡cMIU ‡f013579687 ‡pmdp.39015089706546 ‡sMIU ‡1990135796870106381
974 ⊔ ⊔ ‡bMIU ‡cMIU ‡d20231112 ‡sgoogle ‡umdp.39015089706546 ‡y2014 ‡ric ‡qbib ‡tUS bib date1 >= 1929