On cohomology groups appearing in geometric quantization

1977 ◽  
pp. 46-66 ◽  
Author(s):  
Jedrzej Śniatycki
Keyword(s):  
Geometric Quantization ◽  
Cohomology Groups

On Homology and Cohomology Groups of Remainders

2004 ◽  
Vol 11 (4) ◽  
pp. 613-633
Author(s):  
V. Baladze ◽  
L. Turmanidze
Keyword(s):  
Uniform Space ◽  
Cohomology Groups ◽  
Uniform Spaces ◽  
Intrinsic Characterization

Abstract Border homology and cohomology groups of pairs of uniform spaces are defined and studied. These groups give an intrinsic characterization of Čech type homology and cohomology groups of the remainder of a uniform space.

scholarly journals Degree three unramified cohomology groups

2016 ◽  
Vol 458 ◽  
pp. 120-133 ◽  
Author(s):  
Akinari Hoshi ◽  
Ming-chang Kang ◽  
Aiichi Yamasaki
Keyword(s):  
Cohomology Groups ◽  
Unramified Cohomology

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

scholarly journals Loop Schrödinger–Virasoro Lie conformal algebra

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.

Remarks on the geometric quantization of the Kepler problem

1988 ◽  
Vol 16 (3) ◽  
pp. 189-197 ◽  
Author(s):  
Giuseppe Gaeta ◽  
Mauro Spera
Keyword(s):  
Kepler Problem ◽  
Geometric Quantization

Frölicher–Nijenhuis cohomology on G2- and Spin(7)-manifolds

2018 ◽  
Vol 29 (12) ◽  
pp. 1850075
Author(s):  
Kotaro Kawai ◽  
Hông Vân Lê ◽  
Lorenz Schwachhöfer
Keyword(s):  
Riemannian Manifold ◽  
Differential Form ◽  
Kähler Manifold ◽  
Cohomology Groups ◽  
Kahler Manifold ◽  
Partial Description ◽  
Nijenhuis Bracket

In this paper, we show that a parallel differential form [Formula: see text] of even degree on a Riemannian manifold allows to define a natural differential both on [Formula: see text] and [Formula: see text], defined via the Frölicher–Nijenhuis bracket. For instance, on a Kähler manifold, these operators are the complex differential and the Dolbeault differential, respectively. We investigate this construction when taking the differential with respect to the canonical parallel [Formula: see text]-form on a [Formula: see text]- and [Formula: see text]-manifold, respectively. We calculate the cohomology groups of [Formula: see text] and give a partial description of the cohomology of [Formula: see text].

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