TY - JOUR

T1 - Relative Chern character, boundaries and index formulas

AU - Albin, Pierre

AU - Melrose, Richard

N1 - Funding Information:
P. Albin was partially supported by a National Science Foundation postdoctoral fellowship. R. Melrose was partially supported by National Science Foundation grant DMS-0408993.

PY - 2009/9

Y1 - 2009/9

N2 - 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.

AB - 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.

KW - Atiyah-Bott index theorem

KW - Atiyah-Singer index theorem

KW - Boutet de Monvel index theorem

KW - Chern character

KW - boundary value problems

KW - scattering calculus

KW - smooth K-theory

KW - zero calculus

UR - http://www.scopus.com/inward/record.url?scp=83455242553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=83455242553&partnerID=8YFLogxK

U2 - 10.1142/S1793525309000151

DO - 10.1142/S1793525309000151

M3 - Article

AN - SCOPUS:83455242553

SN - 1793-5253

VL - 1

SP - 207

EP - 250

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 3

ER -