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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1227–1236 (Mi semr990)  

Geometry and topology

Rigidity of powers and Kosniowski's conjecture

Z. Lüa, O. R. Musinbc

a School of Mathematical Sciences, Fudan University, 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

Abstract: 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 $14$.

Keywords: Rigidity of powers, circle action, fixed points, Kosniowski's conjecture, multiplicative genus.

Funding Agency Grant Number
National Natural Science Foundation of China 11661131004
11371093
11431009
National Science Foundation DMS-1400876
Russian Foundation for Basic Research 15-01-99563_а
The first author is partially supported by the NSFC grants (No. 11661131004, 11371093 and 11431009). The second author is partially supported by the NSF grant DMS-1400876 and the RFBR grant 15-01-99563.


DOI: https://doi.org/10.17377/semi.2018.15.099

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Bibliographic databases:

Document Type: Article
UDC: 515.14
MSC: 55N22, 57R77
Received February 19, 2017, published October 22, 2018
Language: English

Citation: Z. Lü, O. R. Musin, “Rigidity of powers and Kosniowski's conjecture”, Sib. Èlektron. Mat. Izv., 15 (2018), 1227–1236

Citation in format AMSBIB
\Bibitem{LuMus18}
\by Z.~L\"u, O.~R.~Musin
\paper Rigidity of powers and Kosniowski's conjecture
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1227--1236
\mathnet{http://mi.mathnet.ru/semr990}
\crossref{https://doi.org/10.17377/semi.2018.15.099}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200041}


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