The $${\mathcal {L}}_B$$LB-cohomology on compact torsion-free $$\mathrm {G}_2$$G2 manifolds and an application to ‘almost’ formality
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DOI: 10.1007/s10455-018-9629-x
Abstract: We study a cohomology theory $$H^{\bullet }_{\varphi }$$Hφ∙, which we call the $${\mathcal {L}}_B$$LB-cohomology, on compact torsion-free $$\mathrm {G}_2$$G2 manifolds. We show that $$H^k_{\varphi } \cong H^k_{\mathrm {dR}}$$Hφk≅HdRk for $$k \ne 3, 4$$k≠3,4, but that $$H^k_{\varphi… read more here.
Keywords: torsion free; compact torsion; cohomology; mathrm ... See more keywords
On the Quasi-Endomorphism Rings of Quasi-Decomposable Torsion-Free Abelian Groups of Rank 4 with a Strongly Indecomposable Quasi-Summand of Rank 2
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DOI: 10.1007/s10958-018-3757-5
Abstract: We obtain a description of quasi-endomorphism rings of torsion-free Abelian groups G of rank 4 that are quasi-decomposable into a direct sum of groups A1 and A2 of rank 1 and a strongly indecomposable group… read more here.
Keywords: torsion free; endomorphism rings; groups rank; abelian groups ... See more keywords
Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space
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DOI: 10.1007/s10958-018-3815-z
Abstract: We give a definition of a conformally connected space with an angular metric of an arbitrary signature. We present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of… read more here.
Keywords: torsion free; space; projective space; tensor ... See more keywords
Classification of the congruence classes of $$A_n^5$$ (n ⩾ 6) with 2-torsion free homology
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DOI: 10.1007/s11425-018-9413-y
Abstract: In this paper, we classify the congruence classes of ${\boldsymbol~F}^5_{n(2)}$-polyhedra, i.e., $(n-1)$-connected, at most $(n+5)$-dimensional polyhedra with 2-torsion free homology. The proof relies on the matrix problem technique which was developed in the classification of… read more here.
Keywords: torsion free; congruence classes; classification; free homology ... See more keywords
Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic threefolds
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DOI: 10.1016/j.jalgebra.2022.03.042
Abstract: LO A BSTRACT . We focus on a class of Weierstraß elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically K -trivial surface. We define the notion… read more here.
Keywords: torsion free; slope stable; elliptic threefolds; stable torsion ... See more keywords
Graded torsion-free ????????2(ℂ)-modules of rank 2
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DOI: 10.1142/s0219498822502292
Abstract: In this paper, we explore the possibility of endowing simple infinite-dimensional [Formula: see text]-modules by the structure of graded modules. The gradings on the finite-dimensional simple modules over simple Lie algebras have been studied in… read more here.
Keywords: free modules; torsion free; graded torsion; modules rank ... See more keywords
Rings of quasi-endomorphisms of some direct sums of torsion-free Abelian groups
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DOI: 10.3103/s1066369x17010078
Abstract: We consider a representation of quasi-endomorphisms of Abelian torsion-free groups of rank 4 bymatrices of order 4 over the field of rational numbers Q. We obtain a classification for quasi-endomorphism rings of Abelian torsion-free groups… read more here.
Keywords: torsion free; torsion; quasi endomorphisms; rings quasi ... See more keywords