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.
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https://www.riss.kr/link?id=A103365837
2012
English
KCI등재,SCIE,SCOPUS
학술저널
223-234(12쪽)
1
0
상세조회0
다운로드다국어 초록 (Multilingual 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.
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 (Reference)
1 D. Freed, "Two index theorems in odd dimensions" 6 (6): 317-329, 1998
2 E. Witten, "Two dimensional gauge theories revisited" 9 (9): 303-368, 1992
3 M. F. Atiyah, "The index of elliptic operators III" 87 : 546-604, 1968
4 E. Meinrenken, "Symplectic surgery and the SpincSpinc-Dirac operator" 134 (134): 240-277, 1998
5 H. Duistermaat, "Symplectic reduction and Riemann-Roch for circle actions" 2 (2): 259-266, 1995
6 E. Lerman, "Symplectic cuts" 2 (2): 247-258, 1995
7 S. Fuchs, "Spin-c Quantization, Prequantization and Cutting" University of Toronto 2008
8 H. Lawson, "Spin Geometry, Princeton Mathematical Series, 38" Princeton University Press 1989
9 V. Guillemin, "Signature quantization" 66 (66): 139-168, 2004
10 K. Liu, "Rigidity theorems on odd dimensional manifolds" 5 (5): 1139-1159, 2009
1 D. Freed, "Two index theorems in odd dimensions" 6 (6): 317-329, 1998
2 E. Witten, "Two dimensional gauge theories revisited" 9 (9): 303-368, 1992
3 M. F. Atiyah, "The index of elliptic operators III" 87 : 546-604, 1968
4 E. Meinrenken, "Symplectic surgery and the SpincSpinc-Dirac operator" 134 (134): 240-277, 1998
5 H. Duistermaat, "Symplectic reduction and Riemann-Roch for circle actions" 2 (2): 259-266, 1995
6 E. Lerman, "Symplectic cuts" 2 (2): 247-258, 1995
7 S. Fuchs, "Spin-c Quantization, Prequantization and Cutting" University of Toronto 2008
8 H. Lawson, "Spin Geometry, Princeton Mathematical Series, 38" Princeton University Press 1989
9 V. Guillemin, "Signature quantization" 66 (66): 139-168, 2004
10 K. Liu, "Rigidity theorems on odd dimensional manifolds" 5 (5): 1139-1159, 2009
11 V. Guillemin, "Reduced phase space and Riemann-Roch, Lie theory and geometry" Birkhauser Boston 123 : 305-334, 1994
12 C. da, "Quantization of presymplectic manifolds and circle actions" 352 (352): 525-552, 2000
13 E. Meinrenken, "On Riemann-Roch formulas for multiplicities" 9 : 373-389, 1996
14 M. Vergne, "Multiplicity formula for geometric quantization, Part II" 82 (82): 181-194, 1996
15 M. Vergne, "Multiplicity formula for geometric quantization" 82 (82): 143-179, 1996
16 L. C. Jeffrey, "Localization for nonabelian group actions" 34 (34): 291-327, 1995
17 L. C. Jeffrey, "Localization and quantization conjecture" 36 (36): 647-693, 1997
18 W. Zhang, "Lectures on Chern-weil Theory and Witten Deformations, Nankai Tracks in Mathematics Vol. 4" World Scientific 2001
19 V. Guillemin, "Geometric quantization and multiplicities of group rep- resentations" 67 (67): 515-538, 1982
20 H. Fang, "Equivariant spectral fiow and a Lefschetz theorem on odd-dimensional spin manifolds" 220 (220): 299-312, 2005
21 Y. Tian, "An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg" 132 (132): 229-259, 1998
22 J. D. Lafferty, "A direct geometric proof of Lefschetz fixed point formulas" 329 (329): 571-583, 1992
GENERALIZED SCHWARZ LEMMAS FOR MEROMORPHIC FUNCTIONS
T-STRUCTURE AND THE YAMABE INVARIANT
GEOMETRIC QUANTIZATION OF ODD DIMENSIONAL SPINc MANIFOLDS
학술지 이력
연월일 | 이력구분 | 이력상세 | 등재구분 |
---|---|---|---|
2023 | 평가예정 | 해외DB학술지평가 신청대상 (해외등재 학술지 평가) | |
2020-01-01 | 평가 | 등재학술지 유지 (해외등재 학술지 평가) | |
2010-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2008-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2006-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2004-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2001-07-01 | 평가 | 등재학술지 선정 (등재후보2차) | |
1999-01-01 | 평가 | 등재후보학술지 선정 (신규평가) |
학술지 인용정보
기준연도 | WOS-KCI 통합IF(2년) | KCIF(2년) | KCIF(3년) |
---|---|---|---|
2016 | 0.35 | 0.1 | 0.27 |
KCIF(4년) | KCIF(5년) | 중심성지수(3년) | 즉시성지수 |
0.23 | 0.2 | 0.339 | 0.04 |