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Lectures on Morse theory, old and new. (English) Zbl 0505.58001


MSC:

58-02 Research exposition (monographs, survey articles) pertaining to global analysis
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
57R70 Critical points and critical submanifolds in differential topology
81T08 Constructive quantum field theory
53C05 Connections (general theory)
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[1] 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. · Zbl 0509.14014
[2] Raoul Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248 – 261. · Zbl 0058.09101
[3] R. Bott, The periodicity theorem for the classical groups, Ann. of Math. (2) 70 2 (1959), 179-203.
[4] Raoul Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171 – 206. · Zbl 0074.17202
[5] Detlef Gromoll and Wolfgang Meyer, On differentiable functions with isolated critical points, Topology 8 (1969), 361 – 369. · Zbl 0212.28903
[6] G. Harder, Eine Bemerkung zu einer Arbeit von P. E. Newstead, J. Reine Angew. Math. 242 (1970), 16 – 25 (German). · Zbl 0219.14016
[7] 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. · Zbl 0324.14006
[8] Wilhelm Klingenberg, Lectures on closed geodesics, Springer-Verlag, Berlin-New York, 1978. Grundlehren der Mathematischen Wissenschaften, Vol. 230. · Zbl 0397.58018
[9] L. Lyusternik and L. Schnirelmann, Topological methods in the calculus of variations, Gosndarstv. Izdat. Tehn-Teor. Lit., Moscow, 1930.
[10] P. E. Newstead, Stable bundles of rank 2 and odd degree over a curve of genus 2, Topology 7 (1968), 205 – 215. · Zbl 0174.52901
[11] C. S. Seshadri, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 85 (1967), 303 – 336. · Zbl 0173.23001
[12] Raoul Bott and Hans Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964 – 1029. · Zbl 0101.39702
[13] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747 – 817. · Zbl 0202.55202
[14] René Thom, Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris 228 (1949), 973 – 975 (French). · Zbl 0034.20802
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