The Nikulin congruence for four-dimensional \(M\)-varieties
type: Item
instance of: scholarly article
title: The Nikulin congruence for four-dimensional \(M\)-varieties
zbMATH Open document ID: 1064.14071
author: V. A. Krasnov
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: It is proven that the Euler characteristic of a real non-singular algebraic \(M\)-variety (i.e., such that the total \({\mathbb Z}/2\) Betti number of the real point set is equal to the total \({\mathbb Z}/2\) Betti number of the complexification) is divisible by \(2^{m+3}\), provided that the Euler characteristic of any connected component of the real point set is divisible by \(2^m\), and a few more conditions are fulfilled. The claim is generalized to smooth \(8\)-dimensional manifolds with an orientation-preserving involution. Such a statement for real non-singular \(M\)-surfaces has been established by \textit{V. Nikulin} [Math. USSR, Izv. 22, 99--172 (1984; Zbl 0547.10021)]. The proof is based on the technique of the equivariant cohomology of topological spaces with involution.
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 2121458
zbMATH Keywords: congruences for the Euler characteristic
zbMATH Keywords: equivariant homology and cohomology
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
full work available at URL: b:matn.0000036757.67922.0a
OpenAlex ID: W2069714453
DOI: 10.1023/B:MATN.0000036757.67922.0A
description: scientific article; zbMATH DE number 2121458