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We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (≡ APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative index theorem for the difference of two APS-index classes associated to differe...

Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...

Gender identification application of Music Information Retrieval (MIR) research requires that the audio features that are extracted from the sound files should be sufficiently strong to be able to correctly classify the singer into male or a female. In literature, a lot of such applications are developed for speaker’s gender identification. Unfortunately, these applications cannot be applied fo...

This paper is a continuation of [1], where we have studied a general class of (pseudo)differential operators with nonlocal coefficients, referred to as operators with shifts, and obtained a local index formula (i.e., a formula expressing the index as the integral of a differential form explicitly determined by the principal symbol of the operator) for matrix elliptic operators of this kind. In ...

For a family of Dirac operators acting on Hermitian Cli ord modules over the odd dimensional compact manifolds with boundary which are the bres of a bration with compact base we compute the Chern character of the index in K of the base Although we assume a product decomposition near the boundary we make no assumptions on invertibility of the bound ary family and instead obtain a family of self ...