TY - JOUR

T1 - The geometry of loop spaces II

T2 - Characteristic classes

AU - Maeda, Yoshiaki

AU - Rosenberg, Steven

AU - Torres-Ardila, Fabián

N1 - Publisher Copyright:
© 2015 Elsevier Inc.

PY - 2016/1/10

Y1 - 2016/1/10

N2 - We develop a theory of Chern-Simons classes CS2k-1W∈H2k-1(LM2k-1;R) on the loop space LM of a Riemannian manifold M. These classes are associated to a pair of connections on LM whose connection and curvature forms take values in pseudodifferential operators by [19]. We use the Wodzicki residue of these operators to define and compute the Chern-Simons classes. As an application, we prove that |π1(Diff(M))|=∞ for the total space M of circle bundles associated to high multiples of a Kähler class over integral Kähler surfaces.

AB - We develop a theory of Chern-Simons classes CS2k-1W∈H2k-1(LM2k-1;R) on the loop space LM of a Riemannian manifold M. These classes are associated to a pair of connections on LM whose connection and curvature forms take values in pseudodifferential operators by [19]. We use the Wodzicki residue of these operators to define and compute the Chern-Simons classes. As an application, we prove that |π1(Diff(M))|=∞ for the total space M of circle bundles associated to high multiples of a Kähler class over integral Kähler surfaces.

KW - Characteristic classes

KW - Diffeomorphism groups

KW - Loop spaces

KW - Pseudodifferential operators

KW - Wodzicki residue

UR - http://www.scopus.com/inward/record.url?scp=84944916842&partnerID=8YFLogxK

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U2 - 10.1016/j.aim.2015.10.001

DO - 10.1016/j.aim.2015.10.001

M3 - Article

AN - SCOPUS:84944916842

VL - 287

SP - 485

EP - 518

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -