Volume of representations and mapping degree

Pierre Derbez; Yi Liu; Hongbin Sun; Shicheng Wang

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arXiv · 1703.07443

Volume of representations and mapping degree

Pierre Derbez·Yi Liu·Hongbin Sun·Shicheng Wang

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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 $\rho\colon \pi_1(M)\to G$ 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.

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Pierre Derbez, Yi Liu, Hongbin Sun, Shicheng Wang. 2017-03-21. Volume of representations and mapping degree. https://arxiv.org/abs/1703.07443

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