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Lectures on Morse theory, old and new
Author:
Raoul Bott
Journal:
Bull. Amer. Math. Soc. 7 (1982), 331-358
MSC (1980):
Primary 58E05
Link to commentary:
Bull. Amer. Math. Soc., 48 (2011), no. 4, 517--523.
MathSciNet review:
663786
Full-text PDF
References |
Similar Articles |
Additional Information
-
M.
F. Atiyah and R.
Bott, The Yang-Mills equations over Riemann surfaces, Philos.
Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505,
523–615. MR
702806 (85k:14006), http://dx.doi.org/10.1098/rsta.1983.0017
-
Raoul
Bott, Nondegenerate critical manifolds, Ann. of Math. (2)
60 (1954), 248–261. MR 0064399
(16,276f)
-
[B2] R. Bott, The periodicity theorem for the classical groups, Ann. of Math. (2) 70 2 (1959), 179-203.
-
Raoul
Bott, On the iteration of closed geodesics and the Sturm
intersection theory, Comm. Pure Appl. Math. 9 (1956),
171–206. MR 0090730
(19,859f)
-
Detlef
Gromoll and Wolfgang
Meyer, On differentiable functions with isolated critical
points, Topology 8 (1969), 361–369. MR 0246329
(39 #7633)
-
G.
Harder, Eine Bemerkung zu einer Arbeit von P. E. Newstead, J.
Reine Angew. Math. 242 (1970), 16–25 (German). MR 0262246
(41 #6856)
-
G.
Harder and M.
S. Narasimhan, On the cohomology groups of moduli spaces of vector
bundles on curves, Math. Ann. 212 (1974/75),
215–248. MR 0364254
(51 #509)
-
Wilhelm
Klingenberg, Lectures on closed geodesics, Springer-Verlag,
Berlin, 1978. Grundlehren der Mathematischen Wissenschaften, Vol. 230. MR 0478069
(57 #17563)
-
[L-S] L. Lyusternik and L. Schnirelmann, Topological methods in the calculus of variations, Gosndarstv. Izdat. Tehn-Teor. Lit., Moscow, 1930.
-
P.
E. Newstead, Stable bundles of rank 2 and odd degree over a curve
of genus 2, Topology 7 (1968), 205–215. MR 0237500
(38 #5782)
-
C.
S. Seshadri, Space of unitary vector bundles on a compact Riemann
surface, Ann. of Math. (2) 85 (1967), 303–336.
MR
0233371 (38 #1693)
-
Raoul
Bott and Hans
Samelson, Applications of the theory of Morse to symmetric
spaces, Amer. J. Math. 80 (1958), 964–1029. MR 0105694
(21 #4430)
-
S.
Smale, Differentiable dynamical
systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 0228014
(37 #3598), http://dx.doi.org/10.1090/S0002-9904-1967-11798-1
-
René
Thom, Sur une partition en cellules associée à une
fonction sur une variété, C. R. Acad. Sci. Paris
228 (1949), 973–975 (French). MR 0029160
(10,558b)
- [A-B] M. Atiyah and R. Bott, On the Yang-Mills equations over Riemann surfaces, Inst. Hautes Études Sci. Publ. Math., Preprint. MR 702806
- [BI] R. Bott, Nondegenerate critical manifold, Ann. of Math. (2) 60 ( 1954), 248-261. MR 64399
- [B2] R. Bott, The periodicity theorem for the classical groups, Ann. of Math. (2) 70 2 (1959), 179-203.
- [B3] R. Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171-206. MR 90730
- [G-M] D. Gromoll and W. Meyer, On differentiable functions with isolated critical points. Topology 8 ( 1969), 361-369. MR 246329
- [H] G. Harder, Eine Bemerkung Zu einer Arbeit von P. E. Newstead, J. für Math. 242 (1970), 16-25. MR 262246
- [H-N] G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles over curves, Math. Ann. 212 (1975), 215-248. MR 364254
- [K] W. Klingenberg, Lectures on closed geodesics, Die Grundlehren der Mat. Wissenschaften, vol. 230, Springer-Verlag, Berlin and New York, 1978. MR 478069
- [L-S] L. Lyusternik and L. Schnirelmann, Topological methods in the calculus of variations, Gosndarstv. Izdat. Tehn-Teor. Lit., Moscow, 1930.
- [N] P. E. Newstead, Stable bundles of rank 2 and odd degree over a curve of genus 2, Topology 7 (1968), 205-215. MR 237500
- [S] C. S. Seshadri, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math. (2)85 (1967), 303-336. MR 233371
- [S-B] H. Samelson and R. Bott, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1968), 965-1029. MR 105694
- [S-S] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 228014
- [T] R. Thorn, Sur une partition en cellules associée aune fonction sur une varitè, C. R. Acad. Sci. Paris Sér. A-B 228 (1949), 973-975. MR 29160
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1982-15038-8
PII:
S 0273-0979(1982)15038-8
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