Communications in Mathematical Physics

, Volume 329, Issue 1, pp 295–323 | Cite as

tt*-Geometry on the Big Phase Space



The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendants, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space.

Using the approach of Dijkgraaf and Witten (Nucl Phys B 342:486–522, 1990), we lift various geometric structures of the small phase space to the big phase space. The main results of our paper state that various notions from tt*-geometry are preserved under such liftings.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Research Unit 4BucharestRomania
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

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