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Geometry Becomes Complex

  • Pietro Giuseppe Fré
Chapter

Abstract

In our conceptual journey from the algebraic notions to the geometrical ones, journey that may be deemed to be the very heart of the present history essay, we have vastly emphasized the idea that groups exist abstractly as algebraic structures, yet are concretely realized as symmetries of geometrical structures, in particular of smooth manifolds. Conversely, possible geometries can be characterized in terms of the symmetries they admit, i.e. of the groups of transformations that preserve some of their fundamental properties.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of TorinoTurinItaly

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