Pfaffian of Appell's Hypergeometric System $\mathcal F_4$ in Terms of the Intersection Form of Twisted Cohomology Groups

2016 ◽  
Vol 52 (2) ◽  
pp. 223-247 ◽  
Author(s):  
Yoshiaki Goto ◽  
Jyoichi Kaneko ◽  
Keiji Matsumoto
Keyword(s):  
Cohomology Groups ◽  
Intersection Form ◽  
Twisted Cohomology

Computing Bases of Twisted Cohomology Groups for Sparse Polynomials

2015 ◽  
Vol 48 (3/4) ◽  
pp. 118-120 ◽  
Author(s):  
Takayuki Hibi ◽  
Kenta Nishiyama ◽  
Nobuki Takayama
Keyword(s):  
Cohomology Groups ◽  
Twisted Cohomology ◽  
Sparse Polynomials

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

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 Entropy and twisted cohomology

Topology ◽  
1986 ◽  
Vol 25 (4) ◽  
pp. 455-470 ◽  
Author(s):  
David Fried
Keyword(s):  
Twisted Cohomology

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 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.

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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