Morse-Bott homology
Morse-Bott homology
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莫尔斯-博特同源性
DOI：
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发表时间：
2006
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影响因子：
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通讯作者：
D. Hurtubise
中科院分区：
文献类型：
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作者：
A. Banyaga;D. Hurtubise
我们通过构造一个与Morse-Bott-Smer函数相关的链复形给出了Morse同调定理的一个新的证明，当该函数是Morse-Smer时，它退化为Morse-Smer-Witten链复形，当该函数不变时，我们构造了光滑奇异N-立方体链的链复形。利用紧致的含时梯度流线的模空间证明了Floer型延拓定理，证明了链复合体的同调与Morse-Bott-Smer函数无关。
We give a new proof of the Morse Homology Theorem by constructing a chain complex associated to a Morse-Bott-Smale function that reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of smooth singular N-cube chains when the function is constant. We show that the homology of the chain complex is independent of the Morse-Bott-Smale function by using compactified moduli spaces of time dependent gradient flow lines to prove a Floer-type continuation theorem.