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pro vyhledávání: '"Suciu, Alexander"'
Autor:
Suciu, Alexander I.
A complex hyperplane arrangement $\mathcal{A}$ is said to be decomposable if there are no elements in the degree 3 part of its holonomy Lie algebra besides those coming from the rank 2 flats. When this purely combinatorial condition is satisfied, it
Externí odkaz:
http://arxiv.org/abs/2404.04784
Publikováno v:
Journal of Algebraic Combinatorics 59 (2024), no. 4, 787-805
Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the (higher) K
Externí odkaz:
http://arxiv.org/abs/2309.00609
In previous work, we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. Given such an $R$-dga, $(A,d_A)$, defined over the ring $R=\ma
Externí odkaz:
http://arxiv.org/abs/2306.11849
Publikováno v:
Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal), 814 (2024), 205--240
The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric contexts. We discuss their scheme structure in a general algebraic setting and introduce various properties that ensure th
Externí odkaz:
http://arxiv.org/abs/2303.07855
Autor:
Suciu, Alexander I.
Publikováno v:
EMS Surveys in Mathematical Sciences 10 (2023), no. 2, 321-403
We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms of the fi
Externí odkaz:
http://arxiv.org/abs/2210.08310
Autor:
Suciu, Alexander I.
Publikováno v:
Compactifications, Configurations, and Cohomology, 131-157, Contemporary Mathematics, vol. 790, Amer. Math. Soc., Providence, RI, 2023
We use the action of the Bockstein homomorphism on the cohomology ring $H^*(X,\mathbb{Z}_2)$ of a finite-type CW-complex $X$ in order to define the resonance varieties of $X$ in characteristic 2. Much of the theory is done in the more general framewo
Externí odkaz:
http://arxiv.org/abs/2205.10716
Autor:
Suciu, Alexander I.
Publikováno v:
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 25 (2024), no. 2, 1085-1154
We study the integral, rational, and modular Alexander invariants, as well as the cohomology jump loci of groups arising as extensions with trivial algebraic monodromy. Our focus is on extensions of the form $1\to K\to G\to Q\to 1$, where $Q$ is an a
Externí odkaz:
http://arxiv.org/abs/2107.05148
Autor:
Suciu, Alexander I.
Following Lazard, we study the $N$-series of a group $G$ and their associated graded Lie algebras. The main examples we consider are the lower central series and Stallings' rational and mod-$p$ versions of this series. Building on the work of Massuye
Externí odkaz:
http://arxiv.org/abs/2105.14129
Publikováno v:
Topology and its Applications 313 (2022), 107987
Motivated by the construction of Steenrod cup-$i$ products in the singular cochain algebra of a space and in the algebra of non-commutative differential forms, we define a category of binomial cup-one differential graded algebras over the integers an
Externí odkaz:
http://arxiv.org/abs/2105.10753
Autor:
Suciu, Alexander I.
Publikováno v:
Mathematische Annalen 380 (2021), no. 3-4, 1427-1463
The Bieri-Neumann-Strebel-Renz invariants $\Sigma^q(X,\mathbb{Z})\subset H^1(X,\mathbb{R})$ of a connected, finite-type CW-complex $X$ are the vanishing loci for Novikov-Sikorav homology in degrees up to $q$, while the characteristic varieties $\math
Externí odkaz:
http://arxiv.org/abs/2010.07499