@article{09169399ba524d838de79ec023124d09,
title = "Volume of representations and mapping degree",
abstract = " Given a connected real Lie group and a contractible homogeneous proper G–space X furnished with a G–invariant volume form, a real valued volume can be assigned to any representation ρ:π 1 (M)→G for any oriented closed smooth manifold M of the same dimension as X. Suppose that G contains a closed and cocompact semisimple subgroup, it is shown in this paper that the set of volumes is finite for any given M. From a perspective of model geometries, examples are investigated and applications with mapping degrees are discussed.",
keywords = "Cocompact, Representation volume, Semisimple Lie group",
author = "Pierre Derbez and Yi Liu and Hongbin Sun and Shicheng Wang",
note = "Funding Information: The author Y. L. is partially supported by the Recruitment Program of Global Youth Experts of China. The author H. S. is partially supported by Grant No. DMS-1510383 of the National Science Foundation of the United States. The author S. W. is partially supported by grant No. 11371034 of the National Natural Science Foundation of China.☆ The author Y. L. is partially supported by the Recruitment Program of Global Youth Experts of China. The author H. S. is partially supported by Grant No. DMS-1510383 of the National Science Foundation of the United States. The author S. W. is partially supported by grant No. 11371034 of the National Natural Science Foundation of China. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",
year = "2019",
month = jul,
day = "31",
doi = "10.1016/j.aim.2019.05.015",
language = "English (US)",
volume = "351",
pages = "570--613",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}