Novikov同调与非交换Alexander多项式
Novikov homology and noncommutative Alexander polynomials
摘要：
在2000年初，Cochran和Harvey引入了三维流形的非交换Alexander多项式。它们的度给出了Thurston范数的强下界。本文证明了某个Novikov-Sikorav同调模的零化是一元非交换Alexander多项式的正确概念。此外，我们将利用这个机会给新的证明的几个声明诺维科夫-西科拉夫同源性在三维的背景下。
英文摘要：
In the early 2000's Cochran and Harvey introduced non-commutative Alexander polynomials for 3-manifolds. Their degrees give strong lower bounds on the Thurston norm. In this paper we make the case that the vanishing of a certain Novikov-Sikorav homology module is the correct notion of a monic non-commutative Alexander polynomial. Furthermore we will use the opportunity to give new proofs of several statements about Novikov-Sikorav homology in the three-dimensional context.
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