Homology and Cohomology of Finite Spaces
Carmona S\'anchez, V., Maestro P\'erez, C., Sancho de Salas, F. and, Torres Sancho, J.F
TL;DR
This paper develops foundational theorems like base change, projection formula, and Verdier duality for homology and cohomology theories specifically in finite topological spaces.
Contribution
It introduces new duality and base change results tailored for homology and cohomology in finite spaces, expanding classical algebraic topology tools.
Findings
Established base change theorems for finite spaces
Proved projection formulae in the finite setting
Developed Verdier duality for finite topological spaces
Abstract
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
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