On A Stringy Singular Cohomology
On A Stringy Singular Cohomology
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关于弦奇异上同调
DOI：
10.1142/s0217732397000546
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发表时间：
1996
影响因子：
1.2
通讯作者：
Tristan Hubsch
中科院分区：
文献类型：
--
作者：
Tristan Hubsch
弦理论已经激发、建议、有时几乎证明了许多有趣的、有时是意想不到的数学结果，例如镜像对称性。对(温和的)奇异变种上的弦传播行为的仔细研究类似地提出了一种新的(共)同调理论。它具有已建立的交(上)同调和L 2-上同调的“良好性能”，但在某些方面有明显的不同。ff。首先，与交(上)同调和L 2-上同调(或迄今已知的任何其他上同调)不同，这种新的上同调相对于镜像映射是对称的。在可用的选择中，这使它成为用几何术语描述弦理论零模的主要候选者。
String theory has already motivated, suggested, and sometimes well-nigh proved a number of interesting and sometimes unex-pected mathematical results, such as mirror symmetry. A care-ful examination of the behavior of string propagation on (mildly) singular varieties similarly suggests a new type of (co)homology theory. It has the ‘good behavior’ of the well established intersection (co)homology and L 2 -cohomology, but is markedly different in some aspects. For one, unlike the intersection (co)homology and the L 2 -cohomology (or any other known thus far), this new cohomology is symmetric with respect to the mirror map. Among the available choices, this makes it into a prime candidate for describing the string theory zero modes in geometrical terms.