New York Journal of Mathematics
Volume 23 (2017) 1065-1085


Gabriel C. Drummond-Cole and John Terilla

Homotopy probability theory on a Riemannian manifold and the Euler equation

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Published: August 22, 2017
Keywords: probability, fluids, Riemannian manifolds, homotopy
Subject: 55U35, 58Axx, 58Cxx, 60Axx, 76xx

Homotopy probability theory is a version of probability theory in which the vector space of random variables is replaced with a chain complex. A natural example extends ordinary probability theory on a finite volume Riemannian manifold M.

In this example, initial conditions for fluid flow on M are identified with collections of homotopy random variables and solutions to the Euler equation are identified with homotopies between collections of homotopy random variables.

Several ideas about using homotopy probability theory to study fluid flow are introduced.


The first author was supported by IBS-R003-D1

Author information

Gabriel C. Drummond-Cole:
Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Republic of Korea 37673

John Terilla:
Department of Mathematics, The Graduate Center and Queens College, The City University of New York, USA