TY - JOUR
T1 - Spectral sequences in smooth generalized cohomology
AU - Grady, Daniel
AU - Sati, Hisham
N1 - Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.
PY - 2017/8/3
Y1 - 2017/8/3
N2 - We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be of the Atiyah-Hirzebruch (AHSS) type, where we provide a filtration by the Čech resolution of smooth manifolds. This allows for systematic study of torsion in differential cohomology. We apply this in detail to smooth Deligne cohomology, differential topological complex K-theory and to a smooth extension of integral Morava K-theory that we introduce. In each case, we explicitly identify the differentials in the corresponding spectral sequences, which exhibit an interesting and systematic interplay between (refinements of) classical cohomology operations, operations involving differential forms and operations on cohomology with U(1) coefficients.
AB - We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be of the Atiyah-Hirzebruch (AHSS) type, where we provide a filtration by the Čech resolution of smooth manifolds. This allows for systematic study of torsion in differential cohomology. We apply this in detail to smooth Deligne cohomology, differential topological complex K-theory and to a smooth extension of integral Morava K-theory that we introduce. In each case, we explicitly identify the differentials in the corresponding spectral sequences, which exhibit an interesting and systematic interplay between (refinements of) classical cohomology operations, operations involving differential forms and operations on cohomology with U(1) coefficients.
KW - Atiyah-Hirzebruch spectral sequence
KW - Cohomology operations
KW - Differential cohomology
KW - Generalized cohomology
KW - Smooth cohomology
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U2 - 10.2140/agt.2017.17.2357
DO - 10.2140/agt.2017.17.2357
M3 - Article
AN - SCOPUS:85027546576
SN - 1472-2747
VL - 17
SP - 2357
EP - 2412
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 4
ER -