Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Goffeng, Magnus"'
Autor:
Gimperlein, Heiko, Goffeng, Magnus
We study the geometric significance of Leinster's magnitude invariant. For closed manifolds we find a precise relation with Brylinski's beta function and therefore with classical invariants of knots and submanifolds. In the special case of compact ho
Externí odkaz:
http://arxiv.org/abs/2409.19969
Autor:
Goffeng, Magnus, Helffer, Bernard
In this paper we study the following question: do sub-Laplacian type operators have non-trivial index theory on Carnot manifolds in higher degree of nilpotency? The problem relates to characterizing the structure of the space of hypoelliptic sub-Lapl
Externí odkaz:
http://arxiv.org/abs/2408.00091
This paper introduces heat semigroups of topological Markov chains and Cuntz-Krieger algebras by means of spectral noncommutative geometry. Using recent advances on the logarithmic Dirichlet Laplacian on Ahlfors regular metric-measure spaces, we cons
Externí odkaz:
http://arxiv.org/abs/2406.07416
Autor:
Goffeng, Magnus
We study the index theory of curved Bernstein-Gelfand-Gelfand (BGG) sequences in parabolic geometry and their role in $K$-homology and noncommutative geometry. The BGG-sequences fit into $K$-homology, and we solve their index problem. We provide a co
Externí odkaz:
http://arxiv.org/abs/2406.07033
Building on work of Williams, Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this result, the first and fourth listed authors of the present paper showed th
Externí odkaz:
http://arxiv.org/abs/2310.00415
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower bound to o
Externí odkaz:
http://arxiv.org/abs/2307.16079
Autor:
Goffeng, Magnus, Nest, Ryszard
Publikováno v:
Ann. K-Th. 8 (2023) 221-243
We study the noncommutative geometry of algebras of Lipschitz continuous and H\"older continuous functions where non-classical and novel differential geometric invariants arise. Indeed, we introduce a new class of Hochschild and cyclic cohomology cla
Externí odkaz:
http://arxiv.org/abs/2204.00361
Autor:
Goffeng, Magnus, Kuzmin, Alexey
We study the index theory of hypoelliptic operators on Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipped with a filtration induced from sub-bundles of the tangent bundle. A Heisenberg pseudodifferential operator, elliptic i
Externí odkaz:
http://arxiv.org/abs/2203.04717
We study the geometric significance of Leinster's notion of magnitude for a smooth manifold with boundary of arbitrary dimension, motivated by open questions for the unit disk in $\mathbb{R}^2$. For a large class of distance functions, including embe
Externí odkaz:
http://arxiv.org/abs/2201.11363
Publikováno v:
J. Anal. Math. 153 (2024), 401-487
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using rec
Externí odkaz:
http://arxiv.org/abs/2201.11357