TY - JOUR
T1 - Stable homology of surface diffeomorphism groups made discrete
AU - Nariman, Sam
N1 - Funding Information:
Acknowledgments It is my pleasure to thank my thesis advisor, Søren Galatius, for his patience, encouragement and technical support during this project. Without his help and support, this paper would not have existed. I also would like to thank Oscar Randal-Williams for many sage remarks. I would like to thank Alexander Kupers for reading the first draft of this paper and Jonathan Bowden for pointing out to me an obstruction for a codimension-2 foliation on a 4–manifold to be foliated cobordant to a flat surface bundle. I am also very grateful to the referee, whose many helpful comments improve the exposition of the paper. This work was partially supported by NSF grants DMS-1105058 and DMS-1405001.
Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.
PY - 2017/8/15
Y1 - 2017/8/15
N2 - We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that C∞-diffeomorphisms of surfaces as family of discrete groups exhibit homological stability. We show that the stable homology of C∞-diffeomorphisms of surfaces as discrete groups is the same as homology of certain infinite loop space related to Haefliger’s classifying space of foliations of codimension 2. We use this infinite loop space to obtain new results about (non)triviality of characteristic classes of flat surface bundles and codimension-2 foliations.
AB - We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that C∞-diffeomorphisms of surfaces as family of discrete groups exhibit homological stability. We show that the stable homology of C∞-diffeomorphisms of surfaces as discrete groups is the same as homology of certain infinite loop space related to Haefliger’s classifying space of foliations of codimension 2. We use this infinite loop space to obtain new results about (non)triviality of characteristic classes of flat surface bundles and codimension-2 foliations.
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U2 - 10.2140/gt.2017.21.3047
DO - 10.2140/gt.2017.21.3047
M3 - Article
AN - SCOPUS:85028327021
SN - 1465-3060
VL - 21
SP - 3047
EP - 3092
JO - Geometry and Topology
JF - Geometry and Topology
IS - 5
ER -