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In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
In this paper, we prove that unit ideal-stable range condition is right and left symmetric.
Motivated by a renewed interest for the “additive dilogarithm” appeared recently, the purpose of this paper is to complete calculations on the tangent complex to the Bloch-Suslin complex, initiated a long time ago and which were motivated at the time by scissors congruence of polyedra and homology of . The tangent complex to the trilogarithmic complex of Goncharov is also considered.
We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and -torsion of mapping tori. We examine its behaviour under fibrations.
For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.
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