Mapping cylinders and the Oka principle Finnur Larusson 32Q2818F2018G3018G5532E1055U35homotopy theorymodel structureprestackmapping cylindercomplex analysisStein manifoldelliptic manifoldsubelliptic manifoldOka PrincipleOka propertyJouanolou Trick We apply concepts and tools from abstract homotopy theory to complex analysis and geometry, continuing our development of the idea that the Oka Principle is about fibrancy in suitable model structures. We explicitly factor a holomorphic map between Stein manifolds through mapping cylinders in three different model structures and use these factorizations to prove implications between ostensibly different Oka properties of complex manifolds and holomorphic maps. We show that for Stein manifolds, several Oka properties coincide and are characterized by the geometric condition of ellipticity. Going beyond the Stein case to a study of cofibrant models of arbitrary complex manifolds, using the Jouanolou Trick, we obtain a geometric characterization of an Oka property for a large class of manifolds, extending our result for Stein manifolds. Finally, we prove a converse Oka Principle saying that certain notions of cofibrancy for manifolds are equivalent to being Stein. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2731 10.1512/iumj.2005.54.2731 en Indiana Univ. Math. J. 54 (2005) 1145 - 1160 state-of-the-art mathematics http://iumj.org/access/