A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology

被引：0
|
作者：
Flydal, Peter Marius [1 ]
Quick, Gereon [1 ]
Svanes, Eirik Eik [2 ]
机构：
[1] NTNU, Dept Math Sci, Trondheim, Norway
[2] Univ Stavanger, Dept Math & Phys, Stavanger, Norway
来源：
ACTA MATHEMATICA VIETNAMICA | 2024年 / 49卷 / 02期
关键词：
Deligne cohomology; Equivariant connection; Classification of vector bundles; GEOMETRY;
D O I：
10.1007/s40306-024-00538-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with Real connection on manifolds with involution.
引用
收藏
页码：187 / 199
页数：13
相关论文
共 14 条
  • [1] Twisted smooth Deligne cohomology
    Grady, Daniel
    Sati, Hisham
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2018, 53 (03) : 445 - 466
  • [2] Twisted smooth Deligne cohomology
    Daniel Grady
    Hisham Sati
    Annals of Global Analysis and Geometry, 2018, 53 : 445 - 466
  • [3] A K-theoretic interpretation of real Deligne cohomology
    Pridham, J. P.
    ADVANCES IN MATHEMATICS, 2017, 320 : 795 - 826
  • [4] HIGHER-TWISTED PERIODIC SMOOTH DELIGNE COHOMOLOGY
    Grady, Daniel
    Sati, Hisham
    HOMOLOGY HOMOTOPY AND APPLICATIONS, 2019, 21 (01) : 129 - 159
  • [5] PARABOLIC BUNDLES OVER THE PROJECTIVE LINE AND THE DELIGNE-SIMPSON PROBLEMS
    Soibelman, Alexander
    QUARTERLY JOURNAL OF MATHEMATICS, 2016, 67 (01) : 75 - 108
  • [6] THE COMPLETENESS OF THE REAL LINE
    Moore, Matthew E.
    CRITICA-REVISTA HISPANOAMERICANA DE FILOSOFIA, 2007, 39 (117): : 61 - 86
  • [7] On the Gauss-Bonnet-Chern formula for real Finsler vector bundles
    Zhao, Wei
    Yuan, Lixia
    Shen, Yibing
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 47 : 43 - 56
  • [8] Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group
    Biquard, Olivier
    Garcia-Prada, Oscar
    Mundet I Riera, Ignasi
    ADVANCES IN MATHEMATICS, 2020, 372
  • [9] Computing roadmaps in unbounded smooth real algebraic sets I: Connectivity results
    Prebet, Remi
    El Din, Mohab Safey
    Schost, Eric
    JOURNAL OF SYMBOLIC COMPUTATION, 2024, 120
  • [10] Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line
    Bauer, Martin
    Bruveris, Martins
    Michor, Peter W.
    JOURNAL OF NONLINEAR SCIENCE, 2014, 24 (05) : 769 - 808
12