scholarly journals NONTRIVIAL CLASSES IN H*(Imb(S1,ℝn)) FROM NONTRIVALENT GRAPH COCYCLES

2004 ◽  
Vol 01 (05) ◽  
pp. 639-650 ◽  
Author(s):  
RICCARDO LONGONI

We construct nontrivial cohomology classes of the space Imb (S1,ℝn) of imbeddings of the circle into ℝn by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number n≥4, a de Rham cohomology class on Imb (S1,ℝn). We prove nontriviality of these classes by evaluation on the dual cycles.

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ali H. Alkhaldi ◽  
Aliya Naaz Siddiqui ◽  
Kamran Ahmad ◽  
Akram Ali

In this article, we discuss the de Rham cohomology class for bislant submanifolds in nearly trans-Sasakian manifolds. Moreover, we give a classification of warped product bislant submanifolds in nearly trans-Sasakian manifolds with some nontrivial examples in the support. Next, it is of great interest to prove that there does not exist any doubly warped product bislant submanifolds other than warped product bislant submanifolds in nearly trans-Sasakian manifolds. Some immediate consequences are also obtained.


2017 ◽  
Vol 28 (09) ◽  
pp. 1740004 ◽  
Author(s):  
Antonio Alarcón ◽  
Finnur Lárusson

Let [Formula: see text] be a connected open Riemann surface. Let [Formula: see text] be an Oka domain in the smooth locus of an analytic subvariety of [Formula: see text], [Formula: see text], such that the convex hull of [Formula: see text] is all of [Formula: see text]. Let [Formula: see text] be the space of nondegenerate holomorphic maps [Formula: see text]. Take a holomorphic 1-form [Formula: see text] on [Formula: see text], not identically zero, and let [Formula: see text] send a map [Formula: see text] to the cohomology class of [Formula: see text]. Our main theorem states that [Formula: see text] is a Serre fibration. This result subsumes the 1971 theorem of Kusunoki and Sainouchi that both the periods and the divisor of a holomorphic form on [Formula: see text] can be prescribed arbitrarily. It also subsumes two parametric h-principles in minimal surface theory proved by Forstnerič and Lárusson in 2016.


2007 ◽  
Vol 04 (04) ◽  
pp. 669-705 ◽  
Author(s):  
ANDREA SPIRO

The inverse problem of the Calculus of Variations for Lagrangians and Euler–Lagrange equations invariant under a pseudogroup [Formula: see text] of local transformations of the base manifold is considered. Exploiting some ideas of Krupka, a theorem is proved showing that, if the configuration space consists of sections of tensor bundles or of local maps of a manifold into another, then such inverse problem is solvable whenever a certain cohomology class of [Formula: see text]-invariant forms on the configuration space is vanishing. In addition, for a few pseudogroups, the cohomology groups considered in the main result are explicitly determined in terms of the de Rham cohomology of the configuration space.


2016 ◽  
Vol 64 (2) ◽  
pp. 109-113
Author(s):  
Saraban Tahora ◽  
Khondokar M Ahmed

In the present paper some aspects of exterior derivative, graded algebra, cohomology algebra, de Rham cohomology algebra, singular homology, cohomology class are studied. Graded subspace, smooth map, a singular P- - simplex in a manifold M, oriented n- manifold M, the space of P- cycles and P- boundaries, Pth singular homology and homology class are treated in our paper. A theorem 3.03 is established which is related to orientable manifold. Dhaka Univ. J. Sci. 64(2): 109-113, 2016 (July)


1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin

Author(s):  
Federico Scavia

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .


2018 ◽  
Vol 154 (4) ◽  
pp. 850-882
Author(s):  
Yunqing Tang

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of$\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus’ prediction for some families of abelian varieties. These families include geometrically simple abelian varieties of prime dimension that have non-trivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture.


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