Bott, Raoul Lectures on Morse theory, old and new. (English) Zbl 0505.58001 Bull. Am. Math. Soc., New Ser. 7, 331-358 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 97 Documents 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) Keywords:closed geodesics; equivariant Morse theory; Yang-Mills functinal; index of geodesics PDFBibTeX XMLCite \textit{R. Bott}, Bull. Am. Math. Soc., New Ser. 7, 331--358 (1982; Zbl 0505.58001) Full Text: DOI References: [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 · doi:10.1098/rsta.1983.0017 [2] Raoul Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248 – 261. · Zbl 0058.09101 · doi:10.2307/1969631 [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 · doi:10.1002/cpa.3160090204 [5] Detlef Gromoll and Wolfgang Meyer, On differentiable functions with isolated critical points, Topology 8 (1969), 361 – 369. · Zbl 0212.28903 · doi:10.1016/0040-9383(69)90022-6 [6] G. Harder, Eine Bemerkung zu einer Arbeit von P. E. Newstead, J. Reine Angew. Math. 242 (1970), 16 – 25 (German). · Zbl 0219.14016 · doi:10.1515/crll.1970.242.16 [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 · doi:10.1007/BF01357141 [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 · doi:10.1016/0040-9383(68)90001-3 [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 · doi:10.2307/1970444 [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 · doi:10.2307/2372843 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.