Reidemeister torsion and the classification of lens spaces

Taams, Lucas (2022) Reidemeister torsion and the classification of lens spaces. Bachelor's Thesis, Mathematics.

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Abstract

Given coprime integers p and q we define the lens space L(p, q) as a quotient of S3. A lens space L(p, q) is a 3-manifold with fundamental group isomorphic to Z/pZ. We show that two lens spaces L(p, q) and L(p, q′) are homeomorphic if and only if q′ = ±q±1 mod p. The sufficient condition is shown by constructing homeomorphisms between the lens spaces. The necessary condition is shown using a technique called Reidemeister torsion, which is a topological invariant. We give concrete calculations of Reidemeister torsion for the circle, the torus and the lens spaces. This quantity is then used to show the necessary condition of the classification. Lastly we show that only the fundamental group and the first homology group depend on the parameter p and that the higher homotopy are equal to those of S3 and the higher homology groups do not depend on p and q.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Veen, R.I. van der and Seri, M.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	14 Jul 2022 11:50
Last Modified:	14 Jul 2022 11:50
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/27799

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