Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Bohlen, Karsten"'
Autor:
Bohlen, Karsten
We model systems as objects in a certain ambient Grothendieck site with additional structure. We introduce generalized sheaves, called virtual manifolds. These sheaves reconstruct an internal groupoid which models instances of the holonomy groupoid o
Externí odkaz:
http://arxiv.org/abs/2103.14117
Autor:
Bohlen, Karsten, Lescure, Jean-Marie
We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associ
Externí odkaz:
http://arxiv.org/abs/1904.04069
Autor:
Bohlen, Karsten
We consider bisingular pseudodifferential operators which are pseudodifferential operators of tensor product type. These operators are defined on the product manifold $M_1 \times M_2$, for closed manifolds $M_1$ and $M_2$. We prove a topological inde
Externí odkaz:
http://arxiv.org/abs/1812.05427
Autor:
Bohlen, Karsten, Schulz, René
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category of compac
Externí odkaz:
http://arxiv.org/abs/1710.02294
Autor:
Bohlen, Karsten
We investigate the problem of calculating the Fredholm index of a geometric Dirac operator subject to local (e.g. Dirichlet and Neumann) and non-local (APS) boundary conditions posed on the strata of a manifold with corners. The boundary strata of th
Externí odkaz:
http://arxiv.org/abs/1704.00535
Autor:
Bohlen, Karsten, Schrohe, Elmar
We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the p
Externí odkaz:
http://arxiv.org/abs/1607.07039
Autor:
Bohlen, Karsten
We describe how Lie groupoids are used in singular analysis, index theory and non-commutative geometry and give a brief overview of the theory. We also expose groupoid proofs of the Atiyah-Singer index theorem and discuss the Baum-Connes conjecture f
Externí odkaz:
http://arxiv.org/abs/1601.04166
Autor:
Bohlen, Karsten
We introduce and study a general pseudodifferential calculus for boundary value problems on a class of non-compact manifolds with boundary (so-called Lie manifolds with boundary). This is accomplished by constructing a suitable generalization of the
Externí odkaz:
http://arxiv.org/abs/1507.01543
Autor:
Bohlen, Karsten
In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace property for the
Externí odkaz:
http://arxiv.org/abs/1506.04180
Autor:
Bohlen, Karsten
We construct a Boutet de Monvel calculus for general pseudodifferential boundary value problems defined on a broad class of non-compact manifolds, the class of so-called Lie manifolds with boundary. It is known that this class of non-compact manifold
Externí odkaz:
http://arxiv.org/abs/1505.07882