dorsal/arxiv
View SchemaOn Ohtsuki's invariants of integral homology 3-spheres, I
| Authors | Xiao-Song Lin, Zhenghan Wang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9509009 |
| URL | https://arxiv.org/abs/q-alg/9509009 |
Abstract
An attempt is made to conceptualize the derivation as well as to facilitate the computation of Ohtsuki's rational invariants $\lambda_n$ of integral homology 3-spheres extracted from Reshetikhin-Turaev SU(2) quantum invariants. Several interesting consequences will follow from our computation of $\lambda_2$. One of them says that $\lambda_2$ is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that $\lambda_{1}$ is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained from surgery on knots by using the Jones polynomial.
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"abstract": "An attempt is made to conceptualize the derivation as well as to facilitate\nthe computation of Ohtsuki\u0027s rational invariants $\\lambda_n$ of integral\nhomology 3-spheres extracted from Reshetikhin-Turaev SU(2) quantum invariants.\nSeveral interesting consequences will follow from our computation of\n$\\lambda_2$. One of them says that $\\lambda_2$ is always an integer divisible\nby 3. It seems interesting to compare this result with the fact shown by\nMurakami that $\\lambda_{1}$ is 6 times the Casson invariant. Other consequences\ninclude some general criteria for distinguishing homology 3-spheres obtained\nfrom surgery on knots by using the Jones polynomial.",
"arxiv_id": "q-alg/9509009",
"authors": [
"Xiao-Song Lin",
"Zhenghan Wang"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "On Ohtsuki\u0027s invariants of integral homology 3-spheres, I",
"url": "https://arxiv.org/abs/q-alg/9509009"
},
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