3 Axioms and more index formulas 165

This is a survey article featuring the general index locality principle introduced by the authors, which can be used to obtain index formulas for elliptic operators and Fourier integral operators in various situations, including operators on stratified manifolds and manifolds with singularities.

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RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS

Journal of Topology and Analysis ◽

10.1142/s1793525309000151 ◽

2009 ◽

Vol 01 (03) ◽

pp. 207-250 ◽

Cited By ~ 2

Author(s):

PIERRE ALBIN ◽

RICHARD MELROSE

Keyword(s):

Compact Manifold ◽

Pseudodifferential Operators ◽

Chern Character ◽

Explicit Formulas ◽

Manifold With Boundary ◽

Index Bundle ◽

Normal Operators ◽

K Theory ◽

Index Formulas ◽

Character Mapping

For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have "geometric K-theory", namely the "transmission algebra" introduced by Boutet de Monvel [5], the "zero algebra" introduced by Mazzeo in [9, 10] and the "scattering algebra" from [16], we give explicit formulas for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fiber operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of a vector bundle over a manifold with boundary in which the Chern character, mapping from the corresponding realization of K-theory, naturally takes values.

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Maslov index formulas for Whitney $n$-gons

Journal of Symplectic Geometry ◽

10.4310/jsg.2011.v9.n2.a5 ◽

2011 ◽

Vol 9 (2) ◽

pp. 251-270 ◽

Cited By ~ 11

Author(s):

Sucharit Sarkar

Keyword(s):

Maslov Index ◽

Index Formulas

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The Index and Spectrum of Lie Poset Algebras of Types B, C, and D

The Electronic Journal of Combinatorics ◽

10.37236/9558 ◽

2021 ◽

Vol 28 (3) ◽

Cited By ~ 1

Author(s):

Vincent Coll ◽

Nicholas W. Mayers ◽

Nicholas Russoniello

Keyword(s):

Lie Algebras ◽

Primary Concern ◽

Type B ◽

Restricted Class ◽

The Matrix ◽

Index Formulas

We define posets of types B, C, and D. These posets encode the matrix forms of certain Lie algebras which lie between the algebras of upper-triangular and diagonal matrices. Our primary concern is the index and spectral theories of such type-B, C, and D Lie poset algebras. For an important restricted class, we develop combinatorial index formulas and, in particular, characterize posets corresponding to Frobenius Lie algebras. In this latter case we show that the spectrum is binary; that is, consists of an equal number of 0's and 1's. Interestingly, type-B, C, and D Lie poset algebras can be related to Reiner's notion of a parset.

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Elementary Index Bias: Evidence for the Euro Area from a Large Scanner Dataset

German Economic Review ◽

10.1111/geer.12182 ◽

2019 ◽

Vol 20 (4) ◽

pp. e618-e656

Author(s):

Enikő Gábor-Tóth ◽

Philip Vermeulen

Keyword(s):

Euro Area ◽

Product Category ◽

Scanner Data ◽

Product Categories ◽

Percentage Points ◽

Price Indexes ◽

Substitution Bias ◽

Upper Level ◽

Index Formulas ◽

Fisher Ideal Index

Abstract We provide evidence on the effect of elementary index choice on inflation measurement in the euro area. Using scanner data for 15,844 individual items from 42 product categories and 10 euro area countries, we compute product category level elementary price indexes using eight different elementary index formulas. Measured inflation outcomes of the different index formulas are compared with the Fisher ideal index to quantify elementary index bias. We have three main findings. First, elementary index bias is quite variable across product categories, countries and index formulas. Second, a comparison of elementary index formulas with and without expenditure weights shows that a shift from price only indexes to expenditure weighted indexes would entail at the product level multiple percentage points differences in measured price changes. And finally, we show that elementary index bias is quantitatively more important than upper level substitution bias.

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