Geography and Botany of Irreducible Symplectic 4-Manifolds with Abelian Fundamental Group

Citation

Torres Ruiz, Rafael (2010) Geography and Botany of Irreducible Symplectic 4-Manifolds with Abelian Fundamental Group. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/A9WD-BN29. https://resolver.caltech.edu/CaltechTHESIS:06082010-161504738

Abstract

In this thesis the geography and botany of irreducible symplectic 4-manifolds with abelian fundamental group of small rank are studied. It resembles an anthology of the contribution obtained by the author during his infatuation with 4-dimensional topology by studying its recent developments. As such, each chapter is independent from each other and the reader is welcomed to start reading whichever one seems more appealing. We now give an outline for the sake of convenience.

The first chapter of the thesis deals with the existence and (lack of) uniqueness of smooth irreducible symplectic non-spin 4-manifolds with cyclic fundamental group (both finite and infinite). Chapter 2 does the same for 4-manifolds with abelian, yet non-cyclic π₁; the use of the homeomorphism criteria on these manifolds due to I. Hambleton and M. Kreck is of interest. In Chapter 3, the Spin geography for abelian fundamental groups of small rank is studied. A couple of subtle relations between simply connected and non-simply connected exotic 4-manifolds are explored through out the fourth chapter.

Chapter 5 gives closure to a question raised in Chapter 4, and describes current research projects pursued by the author. These projects came naturally through the results presented in previous chapters. The thesis ends by describing two research progress that are being pursued. Chapter 6 contains the current situation regarding the geography and botany of spin manifolds with zero signature.

The current state of the joint work of the author with Jonathan Yazinski (at McMaster University at the time of writing) is described in the seventh and final chapter.

Thesis Files