Uncover the latest and most impactful research in Algebraic Topology. Explore pioneering discoveries, insightful ideas and new methods from leading researchers in the field.
The notion of the Bott-Duffin group inverse is introduced in a unital ring \(\mathcal {R}\) R . We thereby extend this concept beyond the set of all \(n\times n\) n × n complex matrices. The properties of this generalized inverse are examined in ...
We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation on any symplectic groupoid \(\mathcal {G} \rightrightarrows M.\)...
We study relative cohomology for logarithmic differential forms and meromorphic forms that are relatively closed with respect to the associated logarithmic foliation. Under suitable Diophantine, geometric, and topological hypotheses, we obtain...
We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we construct a sheaf on ...
In this article, we compute the mapping class group of the total space $$S(\xi )$$ S ( ξ ) of the sphere bundle of a 3-dimensional real vector bundle $$\xi $$ ξ over the complex projective plane $$\mathbb {P}^2$$ P 2 with $$\langle p_1(\xi ),...
There is a natural notion of a subdivision of a lower Eulerian poset called a strong formal subdivision, which abstracts the notion of a polyhedral subdivision of a polytope, or a proper, surjective morphism of fans. We show that there is a...
Topology optimization has become a powerful tool for designing lightweight, high-performance structures, yet most existing approaches do not directly produce geometries suitable for manufacturing. Density- and level-set-based methods generally...
In this article we extended the contraction principle to the complete \(\mathbb {C}^*\) C ∗ -algebra-valued semimetric spaces that fulfill an extra regularity property. Next, we study some properties of quasisymmetric maps in \(\mathbb {C}^*\)...
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric objects). The...
Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by \(\Gamma '(R)\) Γ ′ ( R ) , is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices u and vare...
Incorporating the cartesian morphism lifting property from the theory of fibered categories with the horizontal path lifting property of differential geometric connection structures, we develop a theory of parallel transport on principal Lie 2-group...
Abstract In this paper, we provide a partial solution to the Birman–Williams problem on describing the planetary link of a fibered knot \(K\subset\mathbb S^3\) . Using Nielsen’s classification theory of periodic homeomorphisms of surfaces and its...
Generalised almost complex structures \(\mathcal {J}\) J on transitive Courant algebroids E are studied in terms of their components with respect to a splitting \(E\cong TM \oplus T^*M \oplus \mathcal {G}\) E ≅ T M ⊕ T ∗ M ⊕ G , where Mdenotes the...
The local symplectic theory of integrable systems is fundamental to understand their global theory, as well as the behavior near singularities of fundamental models from classical and quantum mechanics which are known to be integrable, such as the...
Let \(Y(E_n)\) Y ( E n ) denote the moduli space of pairs (S, B) where S is a del Pezzo surface of degree \(9-n\) 9 - n and B is the labeled (marked) sum of its finitely many lines. When \(n=6\) n = 6 , \(Y(E_6)\) Y ( E 6 ) is the classical moduli...
We compute some supersymmetric twists of field theories in twistor space, including the minimal supersymmetric and the chiral algebra twists of supersymmetric self-dual Yang-Mills, and the minimal twist of N \( \mathcal{N} \) = 1 self-dual...
Using André–Quillen homology, we prove an ascent result for different types of complete intersection flat dimensions along an essentially of finite type flat local homomorphism with complete intersection closed fibre. As an application of our...
Topology-role coupling is central to multi-agent formation control, yet its combinatorial complexity makes analytical treatment challenging. We propose a three-tensor framework that separately encodes graph structure, time-varying channel states,...
We carry out a Kovalevskaya analysis of the Riccati hierarchy. We determine all indicial loci and Kovalevskaya exponents and identify a rigid recursive structure governing how free parameters enter Laurent solutions. We further identify a nontrivial...
Let \(M_{n,k}\) M n , k denote the even orthogonal Grassmanian, \(SO(2n) / (U(k) \times SO(2n-2k) )\) S O ( 2 n ) / ( U ( k ) × S O ( 2 n - 2 k ) ) . We study endomorphisms of the rational cohomology algebra of \(M_{n,k}\) M n ,...
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manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an...
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Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata...
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Selecta Mathematica, New Seriesis a peer-reviewed journal addressed to a wide mathematical audience. It accepts well-written high quality papers in...
