>>59
>Wittenのモース理論て簡単にいうとどんなもの？

かめで恐縮ですが
http://en.wikipedia.org/wiki/Morse_homology
Related constructions

Edward Witten came up with a related construction in the early 1980s sometimes known as Morse-Witten theory.
Morse homology can be extended to finite dimensional non-compact or infinite-dimensional manifolds where the index remains finite,
the metric is complete and the function satisfies the Palais-Smale condition, such as the energy functional for geodesics on a Riemannian manifold.
The generalization to situations in which both index and coindex are infinite, but the relative index of any pair of critical points is finite, is known as Floer homology.
Sergei Novikov generalized this construction to a homology theory associated to a closed one-form on a manifold. Morse homology is a special case for the one-form df.
A special case of Novikov's theory is circle-valued Morse theory, which Michael Hutchings and Yi-Jen Lee have connected to Reidemeister torsion and Seiberg-Witten theory.

http://www.tahoiya.org/TopoString/?1.Introduction
TFT(位相的場の理論)の歴史的経緯

TFTは次の二つの論文に端を発します。
?Shwarz[Lett.Math.Phys.2:247-252,1978.]

Ray-Singer torsionという位相不変量があるQFT(場の量子論)の分配関数でかけること。
?Witten[J.Diff.Geom.17:661-692,1982.]

モース理論のSQM(超対称量子力学)による理解。

Wittenの仕事
Wittenはさらに次の論文でIndex定理への応用Nucl.Phys.B202:253,1982.を行い、84年にはholomorphic Morse inequalitiesへの一般化を行います。

Floerの３次元位相幾何学への応用
Wittenの仕事はFloerによって３次元位相幾何学の研究に応用されました。Floer(88,89) Floerの３次元位相幾何学の研究はDonaldsonの４次元位相幾何学の研究Donaldson(83,90)と密接に関係があります。