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Rigidity of powers and Kosniowski’s conjecture. (English. English summary) Zbl 1427.57027
Summary: In this paper we state some problems on rigidity of powers in terms of complex analysis and number-theoretic abstraction, which has a strong topological background for the rigid Hirzebruch genera and Kosniowski’s conjecture of unitary circle actions. However, our statements of these problems are elementary enough and do not require any knowledge of algebraic topology. We shall give the solutions of these problems for some particular cases. As a consequence, we obtain that C. Kosniowski’s conjecture [Lect. Notes Math. 788, 331–339 (1980; Zbl 0433.57016)] holds in the case of dimension $$\leq 10$$ or equal to 14.
##### MSC:
 57S15 Compact Lie groups of differentiable transformations 55M20 Fixed points and coincidences in algebraic topology
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##### References:
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