Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1227–1236
Geometry and topology
Rigidity of powers and Kosniowski's conjecture
Z. Lüa, O. R. Musinbc
a School of Mathematical Sciences,
200433, Shanghai, P.R. China
b IITP RAS, Russia
c University of Texas Rio Grande Valley,
School of Mathematical and Statistical Sciences,
One West University Boulevard, Brownsville, TX, 78520, USA
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 Kosniowski's conjecture holds in the case of dimension $\leq 10$ or equal to $14$.
Rigidity of powers, circle action, fixed points, Kosniowski's conjecture, multiplicative genus.
PDF file (170 kB)
MSC: 55N22, 57R77
Received February 19, 2017, published October 22, 2018
Z. Lü, O. R. Musin, “Rigidity of powers and Kosniowski's conjecture”, Sib. Èlektron. Mat. Izv., 15 (2018), 1227–1236
Citation in format AMSBIB
\by Z.~L\"u, O.~R.~Musin
\paper Rigidity of powers and Kosniowski's conjecture
\jour Sib. \`Elektron. Mat. Izv.
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