'Topological parallel world' constructed by modification of space-time along observables
Eiji Ogasa
TL;DR
This paper proposes a novel concept of a topological vacuum parallel world as a tool for studying submanifolds, offering a new interpretation of observables in topological quantum field theory through space-time modifications.
Contribution
It introduces the concept of a topological vacuum parallel world and links observables in TQFT to topological modifications of space-time, providing new interpretative frameworks.
Findings
Examples related to Alexander polynomial and Jones polynomial.
New interpretation of observables in TQFT.
Potential applications in submanifold research.
Abstract
We introduce a new concept, `(topological) (vacuum) parallel world, ' which is a new tool to research submanifolds. Roughly speaking, `Observables in (T)QFT' is equal to `a (topological) modification of space-time.' In other words, we give a new interpretation of observables. We give some examples associated with the Alexander polynomial, the Jones polynomial.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds