# The Universal Coefficient Theorem and Quantum Field Theory

## A Topological Guide for the Duality Seeker

Part of the Springer Theses book series (Springer Theses)

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Part of the Springer Theses book series (Springer Theses)

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Quantum Field Theory and Topology Algebraic Topology for Physics Universal Coefficient Theorem Homological Algebra ER-EPR Algebraic Geometry Riemann-Roch Theorem Grothendieck's Work Applied in Physics

- DOI https://doi.org/10.1007/978-3-319-46143-4
- Copyright Information Springer International Publishing Switzerland 2017
- Publisher Name Springer, Cham
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-319-46142-7
- Online ISBN 978-3-319-46143-4
- Series Print ISSN 2190-5053
- Series Online ISSN 2190-5061
- Buy this book on publisher's site