Torsions for manifolds with boundary and glueing formulas

Dan Burghelea, Leonid Friedlander, Thomas Kappeler

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We extend the definition of analytic and Reidemeister torsion for closed compact Riemannian manifolds, to compact Riemannian manifolds with boundary (M, ∂M), given a parallel flat bundle F of A - Hilbert modules of finite type and a decomposition of the boundary ∂M = ∂_M ∪∂+M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite (cf. [BFKM]), these torsions are known as the L2-analytic resp. L2-Reidemeister torsions. If the system (M, ∂_M, ∂+M,F) is of determinant class we compute the quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of them. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ principal covering where Γ is a residually finite group, we derive from work of LÜCK (cf. [L3]), that, the system (M, ∂_M, ∂+M, F) is of determinant class (cf. Theorem 5.1 in Appendix A).

Original languageEnglish (US)
Pages (from-to)31-91
Number of pages61
JournalMathematische Nachrichten
Volume208
StatePublished - 1999

Fingerprint

Reidemeister Torsion
Manifolds with Boundary
Torsion
Compact Manifold
Riemannian Manifold
Determinant
Covering
Residually Finite Groups
Analytic Torsion
Hilbert Modules
Gluing
Finite Type
Fundamental Group
Bundle
Disjoint
Quotient
Decompose
Closed
Theorem
Class

Keywords

  • Glueing formulas
  • Manifolds with boundaries
  • Torsions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Torsions for manifolds with boundary and glueing formulas. / Burghelea, Dan; Friedlander, Leonid; Kappeler, Thomas.

In: Mathematische Nachrichten, Vol. 208, 1999, p. 31-91.

Research output: Contribution to journalArticle

Burghelea, Dan ; Friedlander, Leonid ; Kappeler, Thomas. / Torsions for manifolds with boundary and glueing formulas. In: Mathematische Nachrichten. 1999 ; Vol. 208. pp. 31-91.
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