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Botvinnik, Boris Perlmutter, Nathan 2015-08-18T23:01:18Z 2015-08-18T23:01:18Z 2015-08-18 https://hdl.handle.net/1794/19241 Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest. en_US University of Oregon All Rights Reserved. Algebraic topology Diffeomorphism groups Differential topology Singularity Theory Surgery Theory Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregonopen.access