非紧流形上椭圆奇对称算子的\(\mathbb {Z}_2\)值索引

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2024-12-26 DOI:10.1007/s40316-024-00228-5

Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh

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引用次数: 0

摘要

我们研究了具有强迫其指标消失的对称性的椭圆算子。我们研究二级指标，定义模2。我们研究了非紧流形上具有这种对称性的Callias型算子，并建立了Toeplitz算子的Gromov-Lawson相对指标定理、Callias指标定理和Boutet de Monvel指标定理的模2版本。

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On the \(\mathbb {Z}_2\)-valued index of elliptic odd symmetric operators on non-compact manifolds

We investigate elliptic operators with a symmetry that forces their index to vanish. We study the secondary index, defined modulo 2. We examine Callias-type operators with this symmetry on non-compact manifolds and establish mod 2 versions of the Gromov–Lawson relative index theorem, the Callias index theorem, and the Boutet de Monvel’s index theorem for Toeplitz operators.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.