Twisted Calabi–Yau ring spectra, string topology, and gauge symmetry
作者: Ralph L. CohenInbar Klang
刊名: Tunisian Journal of Mathematics, 2020, Vol.2 (1), pp.147-196
来源数据库: Project Euclid
DOI: 10.2140/tunis.2020.2.147
关键词: Hochschild homologyRing spectraString topologyCalabi–Yau algebras
原始语种摘要: In this paper we import the theory of “Calabi–Yau” algebras and categories from symplectic topology and topological field theories, to the setting of spectra in stable homotopy theory. Twistings in this theory will be particularly important. There will be two types of Calabi–Yau structures in the setting of ring spectra: one that applies to compact algebras and one that applies to smooth algebras. The main application of twisted compact Calabi–Yau ring spectra that we will study is to describe, prove, and explain a certain duality phenomenon in string topology. This is a duality between the manifold string topology of Chas and Sullivan (1999) and the Lie group string topology of Chataur and Menichi (2012). This will extend and generalize work of Gruher (2007). Then, generalizing work of...
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  • topology 局部解剖学
  • symmetry 对称
  • topological 拓扑的
  • string 细绳
  • spectra 光谱
  • gauge 测定
  • compute 计算
  • sphere 
  • cotangent 余切
  • describe 叙述