First-order local invariants of stable maps from 3-manifolds to \(\mathbb R^{3}\)
type: Item
instance of: scholarly article
title: First-order local invariants of stable maps from 3-manifolds to \(\mathbb R^{3}\)
zbMATH Open document ID: 1266.57018
published in: Michigan Mathematical Journal
publication date: 2013-03-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mmj/1339011532
review text: The authors study Vassiliev type invariants of stable maps from 3-manifolds to \(\mathbb R^3\). These invariants are locally constant functions on the space of stable maps. The idea of Vassiliev invariants is to relate these functions with the topology of the discriminant set. The authors describe the codimension 1 and codimension 2 degenerations of (multi-) germs from 3-dimensions to 3-dimensions, and hence obtain a complete set of generators for first order Vassiliev invariants. Two of these invariants are related to monosingularities, one to a multisingularity, and one to the Euler charactersitic of a branch set. The authors also describe interesting relations to first order Vassiliev invariants of maps from 2-dimension to 3-dimension (found by Goryunov).
reviewed by: Richárd Rimányi
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 58K65
zbMATH DE Number: 6141583
zbMATH Keywords: Vassiliev invariants
zbMATH Keywords: first order invariants
zbMATH Keywords: stable maps
zbMATH Keywords: 3-manifolds
author: Carmen Romero-Fuster
author: Raúl Oset Sinha
MaRDI profile type: Publication
OpenAlex ID: W1975989203
cites work: Q4305594
cites work: Q4325486
cites work: A Classification of 1-Parameter Families of Map Germs R3 , 0 → R3 , 0 with Applications to Condensation Problems
cites work: Q4533265
cites work: Q4046802
cites work: Q3218835
cites work: Q3123466
cites work: Q5701694
cites work: Fold Maps from the Sphere to the Plane
cites work: Stable maps from surfaces to the plane with prescribed branching data
cites work: Black and white local invariants of mappings from surfaces into three-space
cites work: On topologically stable singular surfaces in a 3-manifold
cites work: On the geometry of simple germs of co-rank 1 maps from ℝ3 to ℝ3
cites work: On contact between submanifolds
cites work: First order local invariants of apparent contours
cites work: Global topological invariants of stable maps from 3-manifolds to \(\mathbb R^{3}\)
cites work: FIRST ORDER SEMI-LOCAL INVARIANTS OF STABLE MAPS OF 3-MANIFOLDS INTO THE PLANE
DOI: 10.1307/MMJ/1339011532
description: scientific article; zbMATH DE number 6141583