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2017 Axioms for higher twisted torsion invariants of smooth bundles
Christopher Ohrt
Algebr. Geom. Topol. 17(6): 3665-3701 (2017). DOI: 10.2140/agt.2017.17.3665

Abstract

This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to satisfy. Higher Franz–Reidemeister torsion and twisted versions of the higher Miller–Morita–Mumford classes will satisfy these axioms. We will show that the space of twisted torsion invariants is two-dimensional or one-dimensional depending on the torsion degree and is spanned by these two classes. The proof will greatly depend on results about the equivariant Hatcher constructions developed in Goodwillie, Igusa and Ohrt (2015).

Citation

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Christopher Ohrt. "Axioms for higher twisted torsion invariants of smooth bundles." Algebr. Geom. Topol. 17 (6) 3665 - 3701, 2017. https://doi.org/10.2140/agt.2017.17.3665

Information

Received: 28 September 2016; Revised: 24 March 2017; Accepted: 9 May 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791659
MathSciNet: MR3709657
Digital Object Identifier: 10.2140/agt.2017.17.3665

Subjects:
Primary: 19J10, 55R40
Secondary: 55R10, 57R80

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 6 • 2017
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