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 language | English (US) |
|---|---|
| Pages (from-to) | 31-91 |
| Number of pages | 61 |
| Journal | Mathematische Nachrichten |
| Volume | 208 |
| State | Published - 1999 |
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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 journal › Article
}
TY - JOUR
T1 - Torsions for manifolds with boundary and glueing formulas
AU - Burghelea, Dan
AU - Friedlander, Leonid
AU - Kappeler, Thomas
PY - 1999
Y1 - 1999
N2 - 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).
AB - 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).
KW - Glueing formulas
KW - Manifolds with boundaries
KW - Torsions
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UR - http://www.scopus.com/inward/citedby.url?scp=0008292459&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0008292459
VL - 208
SP - 31
EP - 91
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
ER -