Moscow Mathematical Journal

Volume 26, Issue 2, April–June 2026 pp. 189–254.

Hodge–de Rham Theory and Analytic Torsion for Spaces with Horn Type Singularities

Authors: Mauro Spreafico (1)
Author institution:(1) Dipartimento di fisica, università di Trento, Trento, Italy, and INFN Trento, Italy

Summary:

We study the global analytic properties of a space $X$ with a horn type singularity. In particular, we introduce some de Rham complex of square integrable forms and we describe its homology and the spectral properties of the associated Hodge–Laplace operator. All this is applied to produce a suitable description of the analytic torsion of $X$ and to prove an extension of the Cheeger–Müller theorem.

2020 Math. Subj. Class. 58J52, 57Q10.

Keywords: Analytic torsion, spaces with isolated singularities, Cheeger–Müller Theorem.

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