By Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky

ISBN-10: 3764386037

ISBN-13: 9783764386030

This publication comprises a suite of unique, refereed examine and expository articles on elliptic elements of geometric research on manifolds, together with singular, foliated and non-commutative areas. the subjects lined contain the index of operators, torsion invariants, K-theory of operator algebras and L^{2}-invariants. the consequences offered during this ebook, that is principally encouraged and prompted via the Atiyah-Singer index theorem, can be of curiosity to graduates and researchers in mathematical physics, differential topology and differential analysis.

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**Additional info for C*-Algebras and Elliptic Theory II**

**Example text**

Although they can be deﬁned for arbitrary base pointed manifolds (M, x0 ) we present the theory only in the case χ(M ) = 0 when the base point is irrelevant. While the complex Ray–Singer torsion and dynamical torsion are new concepts the Milnor–Turaev torsion is not, however our presentation is somehow different from the traditional one. In Section 4 we discuss the algebraic variety of cochain complexes of ﬁnite-dimensional vector spaces and introduce the Milnor torsion as a rational function on this variety.

53 6 Milnor–Turaev and dynamical torsion . . . . . . . . . . . . . . . . . 57 7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 1. Introduction For a ﬁnitely presented group Γ denote by Rep(Γ; V ) the algebraic set of all complex representations of Γ on the complex vector space V .

62 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 1. Introduction For a ﬁnitely presented group Γ denote by Rep(Γ; V ) the algebraic set of all complex representations of Γ on the complex vector space V . For a closed base pointed manifold (M, x0 ) with Γ = π1 (M, x0 ) denote by RepM (Γ; V ) the algebraic closure of RepM 0 (Γ; V ), the Zariski open set of representations ρ ∈ Rep(Γ; V ) so that H ∗ (M ; ρ) = 0.

### C*-Algebras and Elliptic Theory II by Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky

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