본문 바로가기
KERD
논문KCI 등재

GEOMETRIC QUANTIZATION OF ODD DIMENSIONAL SPINc MANIFOLDS

Yong Wang|Jian Wang
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회보 (Bulletin of the KMS)|제49권 제2호|pp. 223-234

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

involutionToeplitz operatorsodd spinc quantizationKostant formulascutting formula
주제분류수학

초록

We prove a Guillemin-Sternberg geometric quantization formula for circle action on odd dimensional $spin^c$-manifolds. We prove two Kostant type formulas in this case. As a corollary, we get a cutting formula for the odd spinc quantization.

Abstract

We prove a Guillemin-Sternberg geometric quantization formula for circle action on odd dimensional $spin^c$-manifolds. We prove two Kostant type formulas in this case. As a corollary, we get a cutting formula for the odd spinc quantization.

참고문헌 (22)

  1. C. da, "Quantization of presymplectic manifolds and circle actions", Trans. Amer. Math. Soc, 352(2), pp.525~552 (2000)
  2. M. F. Atiyah, "The index of elliptic operators III", Ann. of Math. (2), 87, pp.546~604 (1968)
  3. H. Duistermaat, "Symplectic reduction and Riemann-Roch for circle actions", Math. Res. Lett, 2(3), pp.259~266 (1995)
  4. H. Fang, "Equivariant spectral fiow and a Lefschetz theorem on odd-dimensional spin manifolds", Pacific J. Math, 220(2), pp.299~312 (2005)
  5. D. Freed, "Two index theorems in odd dimensions", Commu. Anal. Geom, 6(2), pp.317~329 (1998)
  6. S. Fuchs, "Spin-c Quantization, Prequantization and Cutting", pp.2008
  7. V. Guillemin, "Reduced phase space and Riemann-Roch, Lie theory and geometry", Progr. Math., 123, pp.305~334 (1994), Birkhauser Boston
  8. V. Guillemin, "Geometric quantization and multiplicities of group rep- resentations", Invent. Math, 67(3), pp.515~538 (1982)
  9. V. Guillemin, "Signature quantization", J. Differential Geom, 66(1), pp.139~168 (2004)
  10. L. C. Jeffrey, "Localization and quantization conjecture", Topology, 36(3), pp.647~693 (1997)
  11. L. C. Jeffrey, "Localization for nonabelian group actions", Topology, 34(2), pp.291~327 (1995)
  12. J. D. Lafferty, "A direct geometric proof of Lefschetz fixed point formulas", Trans. Amer. Math. Soc, 329(2), pp.571~583 (1992)
  13. H. Lawson, "Spin Geometry, Princeton Mathematical Series, 38" (1989), Princeton University Press
  14. E. Lerman, "Symplectic cuts", Math. Res. Lett, 2(3), pp.247~258 (1995)
  15. K. Liu, "Rigidity theorems on odd dimensional manifolds", Pure Appl. Math. Q, 5(3), pp.1139~1159 (2009)
  16. E. Meinrenken, "On Riemann-Roch formulas for multiplicities", J. Amer. Math. Soc, 9, pp.373~389 (1996)
  17. E. Meinrenken, "Symplectic surgery and the SpincSpinc-Dirac operator", Adv. Math, 134(2), pp.240~277 (1998)
  18. Y. Tian, "An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg", Invent. Math, 132(2), pp.229~259 (1998)
  19. M. Vergne, "Multiplicity formula for geometric quantization", Part I., Duke Math. J, 82(1), pp.143~179 (1996)
  20. M. Vergne, "Multiplicity formula for geometric quantization, Part II", Duke Math. J, 82(1), pp.181~194 (1996)
  21. E. Witten, "Two dimensional gauge theories revisited", J. Geom. Phys, 9(4), pp.303~368 (1992)
  22. W. Zhang, "Lectures on Chern-weil Theory and Witten Deformations, Nankai Tracks in Mathematics Vol. 4" (2001), World Scientific

관련 논문AI추천

THE SYMMETRY OF spinC DIRAC SPECTRUMS ON RIEMANNIAN PRODUCT MANIFOLDS성찬영, 홍규식대한수학회 · 대한수학회지2015 · 제52권 제5호Primitive Circle Actions on Almost Complex Manifolds with Isolated Fixed Points장동훈영남수학회 · East Asian Mathematical Journal2019 · 제35권 제3호SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES김종수한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제4호On non-displaceable Lagrangian submanifolds in two-step flag varieties김유식대한수학회 · 대한수학회지2023 · 제60권 제5호A simply connected manifold with two symplectic deformation equivalence classes with distinct signs of scalar curvatures김종수대한수학회 · 대한수학회논문집2014 · 제29권 제4호SPIN STRUCTURES ON COMPLEX PROJECTIVE SPACES AND CIRCLE ACTIONS장동훈대한수학회 · 대한수학회보2023 · 제60권 제5호

이 간행물의 다른 논문 (20건)

FUNCTION ALGEBRAS ON BIDISKSKieu Phuong Chi, Nguyen Quang Dieupp. 235-247SENSITIVITY ANALYSIS FOR A CLASS OF IMPLICIT MULTIFUNCTIONS WITH APPLICATIONSMinghua Li, Shengjie Lipp. 249-262SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMSXiao Wen, 이건희pp. 263-270LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACEDan Yangpp. 271-284Hypersurfaces with constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in spheresJiancheng Liu, Yan Weipp. 285-293
원문 보기