Acta Mathematica Sinica, English Series

, Volume 34, Issue 10, pp 1485–1500 | Cite as

Estimates of the Isovariant Borsuk–Ulam Constants of Connected Compact Lie Groups

  • Ikumitsu NagasakiEmail author


The isovariant Borsuk–Ulam constant cG of a compact Lie group G is defined to be the supremum of c such that the inequality
$$c\left( {\dim V - \dim {V^C}} \right) \leqslant \dim W - \dim {W^G}$$
holds whenever there exists a G-isovariant map f: S(V) → S(W) between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk–Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk–Ulam constant G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.


Isovariant map Borsuk–Ulam type theorem Borsuk–Ulam constant transformation groups representation theory 

MR(2010) Subject Classification

57S15 57S25 55M20 22E99 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKyoto Prefectural University of MedicineKyotoJapan

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