1998/09/07 by Marika Taylor-Robinson, Taylor-Robinson, Marika
Computer Science · Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9809040
28 pages, RevTeX
arxiv created 1998/09/07 · arxiv updated 2009/11/30
Many Euclidean Einstein manifolds possess continuous symmetry groups of at least one parameter and we consider here a classification scheme of d dimensional compact manifolds based on the existence of such a one parameter group in terms of the fixed point sets of the isometries. We discuss applications of such a classification scheme, including the geometric interpretation of the entropy; there are intrinsic contributions to the entropy from the volumes of (d-2) dimensional fixed point sets and contributions related to the cohomology structure of the orbit space of the isometry. We consider the relevance of such a decomposition of the entropy in the context of the no boundary proposal and cosmological processes, and generalise the discussion to compact solutions of gravity coupled to scalar and gauge fields.