Browsing 1 - Oberwolfach Preprints (OWP) by MSC "58"
Now showing items 1-12 of 12
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Boundary Conditions for Scalar Curvature
[OWP-2021-01] (Mathematisches Forschungsinstitut Oberwolfach, 2021-01-04)Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite $K$-area. We also characterize the extremal case. ... -
Criteria for Algebraicity of Analytic Functions
[OWP-2018-25] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ... -
Embedding Spaces of Split Links
[OWP-2022-13] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-01)We study the homotopy type of the space $\mathcal{E}(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Inspired by work of Brendle and Hatcher, we introduce a semi-simplicial ... -
An Explicit Formula for the Dirac Multiplicities on Lens Spaces
[OWP-2014-19] (Mathematisches Forschungsinstitut Oberwolfach, 2014)We present a new description of the spectrum of the (spin-) Dirac operator $D$ on lens spaces. Viewing a spin lens space $L$ as a locally symmetric space $\Gamma \setminus Spin(2m)/Spin(2m-1)$ and exploiting the representation ... -
Getzler rescaling via adiabatic deformation and a renormalized local index formula
[OWP-2016-18] (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)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). After introducing a renormalized supertrace on Lie manifolds with spin ... -
Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants
[OWP-2017-35] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature. -
Hight functions on quaternionic Stiefel manifolds
[OWP-2015-10] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)In this note, we study height functions on quaternionic Stiefel manifolds and prove that all these height functions are Morse-Bott. Among them, we characterize the Morse functions and give a lower bound for their number ... -
Lifting Spectral Triples to Noncommutative Principal Bundles
[OWP-2021-02] (Mathematisches Forschungsinstitut Oberwolfach, 2021-01-11)Given a free action of a compact Lie group $G$ on a unital C*-algebra $\mathcal{A}$ and a spectral triple on the corresponding fixed point algebra $\mathcal{A}^G$, we present a systematic and in-depth construction of ... -
Milnor fibre homology via deformation
[OWP-2015-22] (Mathematisches Forschungsinstitut Oberwolfach, 2015)In case of one-dimensional singular locus, we use deformations in order toget refined information about the Betti numbers of the Milnor fibre. -
On the geometry of regular maps from a quasi-projective surface to a curve
[OWP-2013-03] (Mathematisches Forschungsinstitut Oberwolfach, 2013-03-14)We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X. -
On the δ=const Collisions of Singularities of Complex Plane Curves
[OWP-2008-15] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ... -
Real Analyticity is Concentrated in Dimension 2
[OWP-2018-23] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ...