4,965 research outputs found
Fast loops on semi-weighted homogeneous hypersurface singularities
We show the existence of ()-fast loops on semi-weighted
homogeneous hypersurface singularities with weights . In
particular we show that semi-weighted homogeneous hypersurface singularities
have metrical conical structure only if its two low weights are equal
Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane
The main goal of this work is to show that if two weighted homogeneous (but
not homogeneous) function-germs (\C^2,0)\to(\C,0) are bi-Lipschitz
equivalent, in the sense that these function-germs can be included in a
strongly bi-Lipschitz trivial family of weighted homogeneous function-germs,
then they are analytically equivalent
Inner Metric Geometry of Complex Algebraic Surfaces with Isolated Singularities
We produce examples of complex algebraic surfaces with isolated singularities
such that these singularities are not metrically conic, i.e. the germs of the
surfaces near singular points are not bi-Lipschitz equivalent, with respect to
the inner metric, to cones. The technique used to prove the nonexistence of the
metric conic structure is related to a development of Metric Homology. The
class of the examples is rather large and it includes some surfaces of
Brieskorn.Comment: 12 page
Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms
We give partial answers to a metric version of Zariski's multiplicity
conjecture. In particular, we prove the multiplicity of complex analytic
surface (not necessarily isolated) singularities in is a
bi-Lipschitz invariant.Comment: Accepted for publication by the Journal of Topolog
Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann
We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz
normally embedded. We also extend to real subanalytic sets the notion of
reduced tangent cone and we show that subanalytic Lipschitz normally embedded
sets have reduced tangent cones. In particular, we get that Lipschitz normally
embedded complex analytic sets have reduced tangent cones.Comment: The paper was reorganized and also it was added an appendix by Anne
Pichon and Walter D. Neumann. It has 13 pages and 6 figure
A Time-Segmented Consortium Blockchain for Robotic Event Registration
A blockchain, during its lifetime, records large amounts of data, that in a
common usage its kept on its entirety. In a robotics environment, the old
information is useful for human evaluation, or oracles interfacing with the
blockchain but it is not useful for the robots that require only current
information in order to continue their work. This causes a storage problem in
blockchain nodes that have limited storage capacity, such as in the case of
nodes attached to robots that are usually built around embedded solutions. This
paper presents a time-segmentation solution for devices with limited storage
capacity, integrated in a particular robot-directed blockchain called
RobotChain. Results are presented regarding the proposed solution that show
that the goal of restricting each node's capacity is reached without
compromising all the benefits that arise from the use of blockchains in these
contexts, and on the contrary, it allows for cheap nodes to use this
blockchain, reduces storage costs and allows faster deployment of new nodes
On the bi-Lipschitz contact equivalence of plane complex function-germs
In this short note, we consider the problem of bi-Lipschitz contact
equivalence of complex analytic function-germs of two variables. It is
inquiring about the infinitesimal sizes of such function-germs, up to
bi-Lipschitz changes of coordinates. We show that this problem is equivalent to
the problem of the right topological classification.Comment: The second version is substantially modified. 1) We have dropped
section 5 of the first version. 2) The introduction is slightly modified. 3)
Section 3 has been augmented with a correct statement of its main result (now
referred as) Theorem 3.6. as a consequence of new Lemmas 3.1 and 3.2. Is also
now given a proof of Proposition 3.
Collapsing topology of isolated singularities
We proof here the existence of a topological thick and thin decomposition of
any closed definable thick isolated singularity germ in the spirit of the
recently discovered metric thick and thin decomposition of complex normal
surface singularities of [10]. Our thin zone catches exactly the homology of
the family of the links collapsing faster than linearly. Simultaneously we
introduce a class of rigid homeomorphisms more general than bi-Lipschitz ones,
which map the topological thin zone onto the topological thin zone of its
image. As a consequence of this point of view for the class of singularities we
consider we exhibit an equivalent description of the notion of separating sets
in terms of this fast contracting homologyComment: 29 p
On normal embedding of complex algebraic surfaces
We construct examples of complex algebraic surfaces not admitting normal
embeddings (in the sense of semialgebraic or subanalytic sets) with image a
complex algebraic surface.Comment: 5 pages. Submitted to Proceedings of the 10th International Workshop
on Real and Complex Singularitie
Choking horns in Lipschitz Geometry of Complex Algebraic Varieties
We study the Lipschitz Geometry of Complex Algebraic Singularities. For this
purpose we introduce the notion of choking horns. A Choking horn is a family of
cycles on the family of the sections of an algebraic variety by very small
spheres centered at a singular point, such that the cycles cannot be boundaries
of nearby chains. The presence of choking horns is an obstruction to metric
conicalness as we can see with some classical isolated hypersurfaces
singularities which we prove are not metrically conic. We also show that there
exist infinitely countably many singular varieties, which are locally
homeomorphic, but not locally bi-Lipschitz equivalent with respect to the inner
metric.Comment: 11 pages. Appendix by Walter D. Neuman
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