Poincar´e duality and the existence of exotic structures on n-spheres

Maico Felipe Silva Ribeiro; Leandro Nery de Oliveira; Thiago Filipe da Silva

doi:10.14244/lajm.v2i01.25

Authors

Maico Ribeiro Universidade Federal do Espirito Santo
Leandro Oliveira Universidade Federal de São Carlos
Thiago da Silva Universidade Federal do Espírito Santo

DOI:

https://doi.org/10.14244/lajm.v2i01.25

Keywords:

Poincaré duality, Exotic sphere, Milnor fibration

Abstract

Poincar´e duality is a remarkable result in Algebraic Topology. It guarantees the existence of an isomorphism between the homology and cohomology groups of manifolds. We present a survey of the most general version of this result and its most important variations such as the Lefschetz duality and the Alexander duality. We consider an important application of these results in the study of the existence of exotic structures on n-spheres.

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