听到不等价的自旋结构和奇异狄拉克算子的形状
Hearing the shape of inequivalent spin structures and exotic Dirac operators
摘要：
奇异旋量场产生于非平凡拓扑流形$M$上的不等价自旋结构。这在狄拉克算子中引入了一个额外的项，由上同调群$H^1(M,\mathbb{Z}_2)$定义，该上同调群支配一个切赫上同调类。这种形式主义是扩展的任何有限维流形，赋予度量的任意签名。奇异修正热核系数，奇异狄拉克算子的光谱性质的几何不变量的$M$，推导和审查。
英文摘要：
Exotic spinor fields arise from inequivalent spin structures on non-trivial topological manifolds, $M$. This induces an additional term in the Dirac operator, defined by the cohomology group $H^1(M,\mathbb{Z}_2)$ that rules a Cech cohomology class. This formalism is extended for manifolds of any finite dimension, endowed with a metric of arbitrary signature. The exotic corrections to heat kernel coefficients, relating spectral properties of exotic Dirac operators to the geometric invariants of $M$, are derived and scrutinized.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
