Involutions on torus bundles over \(S^ 1\)
type: Item
instance of: scholarly article
title: Involutions on torus bundles over \(S^ 1\)
zbMATH Open document ID: 0571.57028
author: Makoto Sakuma
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: For a matrix A in GL(2,\({\mathbb{Z}})\), \(M_ A\) denotes the torus bundle over \(S^ 1\) whose monodromy matrix is A. As a consequence of theorems of this paper, the author obtains the estimate on the number of non- equivalent symmetries on torus bundles. That is, let \(Inv(M_ A)\) denote the set of all equivalence classes of involutions on \(M_ A\) and \(| S|\) denote the cardinality of S. Then, (1) if \(M_ A\) is an orientable torus bundle, then \(1\leq | Inv(M_ A)| \leq 21\). (2) If \(M_ A\) is a non-orientable torus bundle with tr(A)\(\neq 0\), then \(1\leq | Inv(M_ A)| \leq 7\).
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M12
zbMATH DE Number: 3911321
zbMATH Keywords: torus bundle over \(S^ 1\)
zbMATH Keywords: monodromy matrix
zbMATH Keywords: symmetries on torus bundles
zbMATH Keywords: involutions
MaRDI profile type: Publication
Recommended article: Representing and recognizing torus bundles over \(\mathbb S^1\)
Recommended article: Involution surface bundles over surfaces
Recommended article: An Equivariant Torus Theorem for Involutions
Recommended article: \(L^2\)-torsion invariants of a surface bundle over \(S^1\)
Recommended article: Free involutions on torus semi-bundles and the Borsuk-Ulam theorem for maps into \(\mathbf{R}^n\)
Recommended article: On the Witten–Reshetikhin–Turaev invariants of torus bundles
Recommended article: Q3730665
Recommended article: \(L^ 2\)-torsion invariants and homology growth of a torus bundle over \(S^ 1\).
Recommended article: The twisted Floer homology of torus bundles
Recommended article: Free involutions on \(S ^{1} \times S ^{n }\)
description: scientific article; zbMATH DE number 3911321