TY - JOUR
T1 - Characteristic classes of fiber bundles
AU - Matsuyuki, Takahiro
AU - Terashima, Yuji
N1 - Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.
PY - 2016/11/7
Y1 - 2016/11/7
N2 - In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algebras of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham complex on the base space, and show that the induced map on cohomology groups is independent of the choice of metric. Moreover, we show that, applied to a surface bundle, our construction gives Morita-Miller-Mumford classes.
AB - In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algebras of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham complex on the base space, and show that the induced map on cohomology groups is independent of the choice of metric. Moreover, we show that, applied to a surface bundle, our construction gives Morita-Miller-Mumford classes.
KW - Characteristic classes
KW - Chen expansions
KW - Fiber bundles
UR - http://www.scopus.com/inward/record.url?scp=84995578276&partnerID=8YFLogxK
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U2 - 10.2140/agt.2016.16.3029
DO - 10.2140/agt.2016.16.3029
M3 - Article
AN - SCOPUS:84995578276
SN - 1472-2747
VL - 16
SP - 3029
EP - 3050
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 5
ER -