Zobrazeno 1 - 10
of 138
pro vyhledávání: '"Tibar, Mihai"'
Publikováno v:
Bull. Sci. Math. 197 (2024), Paper 103520
For studying the local topology of maps, one uses deformations which split the singularities into simpler ones while preserving the general fibres. We give conditions under which such conservation holds.
Comment: slight changes of terminology, a
Comment: slight changes of terminology, a
Externí odkaz:
http://arxiv.org/abs/2405.17292
Autor:
Joiţa, Cezar, Tibăr, Mihai
The image of a holomorphic map germ is not necessarily locally open, and it is not always well-defined as a set germ. We find the structure of what becomes the image of a map germ when the target is a surface. We encode it as a decorated tree and we
Externí odkaz:
http://arxiv.org/abs/2403.09844
We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus are locally topologically trivial at the boundary.
Comment: Condition (3) replaced by a weaker one
Comment: Condition (3) replaced by a weaker one
Externí odkaz:
http://arxiv.org/abs/2310.07340
Autor:
Maxim, Laurenţiu, Tibăr, Mihai
Publikováno v:
Journal of Topology 17 (2024), no. 4, e12362
To a complex polynomial function $f$ with arbitrary singularities we associate the number of Morse points in a general linear Morsification $f_{t} := f - t\ell$. We produce computable algebraic formulas in terms of invariants of $f$ for the numbers o
Externí odkaz:
http://arxiv.org/abs/2307.04032
Autor:
Tibăr, Mihai
Publikováno v:
Rev. Roum. Math. Pures Appl. 69 (2024), no. 2, 295-303
The number of Morse points in a Morsification determines the topology of the Milnor fibre of a holomorphic function germ $f$ with isolated singularity. If $f$ has an arbitrary singular locus, then this nice relation to the Milnor fibre disappears. We
Externí odkaz:
http://arxiv.org/abs/2307.04773
Publikováno v:
Journal of Geometry and Physics Volume 194, December 2023, 105025
We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the topology of t
Externí odkaz:
http://arxiv.org/abs/2306.05330
Autor:
Monsalve, Gabriel E., Tibăr, Mihai
We develop two methods for expressing the global index of the gradient of a 2 variable polynomial function $f$: in terms of the atypical fibres of $f$, and in terms of the clusters of Milnor arcs at infinity. These allow us to derive upper bounds for
Externí odkaz:
http://arxiv.org/abs/2303.16496
Autor:
Maxim, Laurentiu, Tibăr, Mihai
Publikováno v:
The Quarterly Journal of Mathematics, Volume 74, Issue 4, December 2023, Pages 1535-1544
A set of Morse numbers is associated to a holomorphic function germ with stratified isolated singularity, extending the classical Milnor number to the setting of a singular base space.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2301.00963
Autor:
Chen, Ying, Tibăr, Mihai
Publikováno v:
REV. ROUMAINE MATH. PURES APPL. 67 (2023), no. 1-2, 9-17
We discuss the most general condition under which a singular local tube fibration exists. We give an application to composition of map germs.
Comment: to appear in: Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees, 2023. A volume dedicate
Comment: to appear in: Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees, 2023. A volume dedicate
Externí odkaz:
http://arxiv.org/abs/2212.05826
Autor:
Maxim, Laurenţiu, Tibăr, Mihai
Publikováno v:
Advances in Applied Mathematics 152 (2024), 102597
Motivated by finding an effective way to compute the algebraic complexity of the nearest point problem for algebraic models, we introduce an efficient method for detecting the limit points of the stratified Morse trajectories in a small perturbation
Externí odkaz:
http://arxiv.org/abs/2210.06022