Geometry and topology of cobondaries

Author(s)

Llohann Dallagnol Sperança

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2012-05-18

Examining board members

Alcibiades Rigas; Claudio Gorodski; Wolfgang Ziller; Marcos Benevenuto Jardim; Tomas Edson Barros

• Advisor: Carlos Eduardo Duran Fernandez; Alcibiades Rigas

Abstract

In this work we study the geometry and topology of manifolds homemorphic, but not diffeomorphic, to the standard sphere Sn, the so called exotic spheres. We realize two of these manifolds as isometric quotients of principal bundles with connection metrics over the constant curved sphere. Through this, we present symmetries in these spaces and explicit examples of diffeomorphisms not isotopic to the identity, using them for the calculation of equivariant homotopy groups. As another application, we prove that, if a homotopy 15-sphere is realizeble as the total space of a linear bundle over the standard 8-sphere, then, it is realizeble as the total space of a linear bundle over the exotic 8-sphere with the same transition maps. In the last chapter we deal with the geometry of pull-back bundles, deducing a necessary condition on the pull-back map for nonnegative curvature of the induced connection metric (AU)

• FAPESP's process: 09/07953-8 - Geometry and Topology of Coboundaries
• Grantee: Llohann Dallagnol Sperança
• Support Opportunities: Scholarships in Brazil - Doctorate