Nonacyclic Reidemeister torsions of manifolds of odd dimension
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910714550026240 |
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| author | Nosaka, Takefumi Yanagida, Koki Wakijo, Naoko |
| author_facet | Nosaka, Takefumi Yanagida, Koki Wakijo, Naoko |
| contents | Given an oriented closed manifold $M$ of odd dimension and a unitary representation $ρ: π_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $ρ$ is not acyclic. As corollaries, we introduce some topological invariants of $M$, which include the nonacyclic extensions of abelian torsions and the Alexander polynomials of links. Further, we propose a volume form of the $\SU(n)$-character varieties of $M$. Moreover, we compute the Reidemeister torsions of some representations of 3-manifolds and compare the works of Farber--Turaev. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10143 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonacyclic Reidemeister torsions of manifolds of odd dimension Nosaka, Takefumi Yanagida, Koki Wakijo, Naoko Geometric Topology Algebraic Topology 19J10, 58K65, 57P10, 15A63 Given an oriented closed manifold $M$ of odd dimension and a unitary representation $ρ: π_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $ρ$ is not acyclic. As corollaries, we introduce some topological invariants of $M$, which include the nonacyclic extensions of abelian torsions and the Alexander polynomials of links. Further, we propose a volume form of the $\SU(n)$-character varieties of $M$. Moreover, we compute the Reidemeister torsions of some representations of 3-manifolds and compare the works of Farber--Turaev. |
| title | Nonacyclic Reidemeister torsions of manifolds of odd dimension |
| topic | Geometric Topology Algebraic Topology 19J10, 58K65, 57P10, 15A63 |
| url | https://arxiv.org/abs/2308.10143 |