Global surgery formula for the Casson-Walker invariant
Global surgery formula for the Casson-Walker invariant
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Casson-Walker 不变量的全局手术公式
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
C. Lescop
中科院分区：
文献类型：
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作者：
C. Lescop
这本书提出了一个新的结果在三维拓扑。众所周知，任何封闭的定向三维流形都可以通过在“S“3中的框架连杆上进行外科手术来获得。在“Global Surgery Formula for the Casson-Walker Invariant“中，描述了“S“3中框架链的函数F，并证明了F一致地定义了闭定向三维流形的不变量lamda（“l”）。“l”然后用先前已知的3-流形的不变量来表示。对于积分同调球，“l”是卡森在1985年引入的不变量，这使他能够解决三维拓扑中的古老而著名的问题。随着第一个Betti数的增加，“l”变得更简单。作为亚历山大多项式和框架链的外科系数的显式函数，函数F以自然的方式扩展到有理同调球面中的框架链。证明了F描述了从有理同调球面出发的任意手术下l的变化。因此，F产生了卡森不变量的全局外科手术公式。
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in "S"3. In "Global Surgery Formula for the Casson-Walker Invariant, " a function F of framed links in "S"3 is described, and it is proven that F consistently defines an invariant, lamda ("l"), of closed oriented 3-manifolds. "l" is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, "l" is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. "l" becomes simpler as the first Betti number increases.As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of "l" under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.