Higher invariants in noncommutative geometry

  • Zhizhang Xie
  • Guoliang YuEmail author


We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.



The authors wish to thank Alain Connes for numerous inspiring discussions. The author “Zhizhang Xie” is partially supported by NSF 1500823, NSF 1800737. The author “Guoliang Yu” is partially supported by NSF 1700021, NSF 1564398.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA
  3. 3.Shanghai Center for Mathematical SciencesShanghaiChina

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