Botvinnik, BorisPerlmutter, Nathan2015-08-182015-08-182015-08-18https://hdl.handle.net/1794/19241Let 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-USAll Rights Reserved.Algebraic topologyDiffeomorphism groupsDifferential topologySingularity TheorySurgery TheoryElectronic Thesis or Dissertation