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過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 担当者 | 河野俊丈 |
|---|
2013年06月06日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Real-valued and circle-valued Morse theory:
an introduction
(ENGLISH)
Andrei Pajitnov 氏 (Univ. de Nantes)
Real-valued and circle-valued Morse theory:
an introduction
(ENGLISH)
[ 講演概要 ]
Classical Morse theory relates the number of critical points of a Morse
function f on a manifold M to the topology of M. The main technical
ingredient of this theory is a chain complex generated by the critical points
of the function. In 1981 S.P. Novikov generalized this theory to the case of
circle-valued Morse functions. In this talk we describe the construction of
both chain complexes, based on the idea of E. Witten (1982), which allows, in
particular, to compute the boundary operators in the Morse complex from
the count of flow lines of the gradient of f. We discuss geometric applications
of these constructions.
Classical Morse theory relates the number of critical points of a Morse
function f on a manifold M to the topology of M. The main technical
ingredient of this theory is a chain complex generated by the critical points
of the function. In 1981 S.P. Novikov generalized this theory to the case of
circle-valued Morse functions. In this talk we describe the construction of
both chain complexes, based on the idea of E. Witten (1982), which allows, in
particular, to compute the boundary operators in the Morse complex from
the count of flow lines of the gradient of f. We discuss geometric applications
of these constructions.
