scholarly journals Tautological rings of stable map spaces

2008 ◽  
Vol 217 (4) ◽  
pp. 1728-1755
Author(s):  
Anca M. Mustaţǎ ◽  
Andrei Mustaţǎ
Keyword(s):  
Stable Map ◽  
Tautological Rings

scholarly journals Tautological rings of spaces of pointed genus two curves of compact type

2016 ◽  
Vol 152 (7) ◽  
pp. 1398-1420 ◽  
Author(s):  
Dan Petersen
Keyword(s):  
Hodge Structure ◽  
Galois Representation ◽  
Mixed Hodge Structure ◽  
Poincaré Duality ◽  
General Study ◽  
Compact Type ◽  
Poincare Duality ◽  
Tautological Ring ◽  
Genus Two ◽  
Tautological Rings

We prove that the tautological ring of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$, the moduli space of $n$-pointed genus two curves of compact type, does not have Poincaré duality for any $n\geqslant 8$. This result is obtained via a more general study of the cohomology groups of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of $H^{k}({\mathcal{M}}_{2,n}^{\mathsf{ct}})$ for any $k$ and $n$ considered both as $\mathbb{S}_{n}$-representation and as mixed Hodge structure/$\ell$-adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of $\overline{{\mathcal{M}}}_{2,n}$ is tautological for $n<20$, and that the tautological ring of $\overline{{\mathcal{M}}}_{2,n}$ fails to have Poincaré duality for all $n\geqslant 20$. This improves and simplifies results of the author and Orsola Tommasi.

scholarly journals Approximation of additive functional equations in NA Lie C*-algebras

2018 ◽  
Vol 51 (1) ◽  
pp. 37-44 ◽  
Author(s):  
Zhihua Wang ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Content Type ◽  
Additive Functional Equation ◽  
C Algebras ◽  
Stable Map ◽  
Higher Derivation

AbstractIn this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation,where m ≥ 2.

A topological invariant for stable map germs

1976 ◽  
Vol 32 (2) ◽  
pp. 103-132 ◽  
Author(s):  
James Damon ◽  
Andr� Galligo
Keyword(s):  
Topological Invariant ◽  
Stable Map

scholarly journals A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Risong Li ◽  
Xiaoliang Zhou
Keyword(s):  
Metric Space ◽  
Compact Metric Space ◽  
Shadowing Property ◽  
Topologically Transitive ◽  
Stable Map ◽  
Asymptotic Average Shadowing

We prove that if a continuous, Lyapunov stable mapffrom a compact metric spaceXinto itself is topologically transitive and has the asymptotic average shadowing property, thenXis consisting of one point. As an application, we prove that the identity mapiX:X→Xdoes not have the asymptotic average shadowing property, whereXis a compact metric space with at least two points.

Cr [Kscr ]-versality of the graph deformation of a Cr stable map-germ

1999 ◽  
Vol 127 (1) ◽  
pp. 93-97 ◽  
Author(s):  
TAKASHI NISHIMURA
Keyword(s):  
Stable Map

In his celebrated paper [7], Martinet showed the equivalence between the infinitesimal versality and the versality for [Ascr ]- and [Kscr ]-morphisms. By using this theorem, he obtained the following Theorem 1·1 which played one of the key roles for the classification of C∞ stable map-germs ([1, 7]).

scholarly journals On the Hilbert-Samuel partition of stable map-germs

1983 ◽  
Vol 79 ◽  
pp. 327-358
Author(s):  
James Damon ◽  
André Galligo
Keyword(s):  
Stable Map

scholarly journals The Reeb Graph of a Map Germ from ℝ3 to ℝ2 with Isolated Zeros

2016 ◽  
Vol 60 (2) ◽  
pp. 319-348 ◽  
Author(s):  
Erica Boizan Batista ◽  
João Carlos Ferreira Costa ◽  
Juan J. Nuño-Ballesteros
Keyword(s):  
Structure Theorem ◽  
Topological Type ◽  
Topological Invariant ◽  
Topological Equivalence ◽  
Stable Maps ◽  
Reeb Graph ◽  
Cone Structure ◽  
Topological Description ◽  
Stable Map

AbstractWe consider finitely determined map germs f : (ℝ3, 0) → (ℝ2, 0) with f–1(0) = {0} and we look at the classification of this kind of germ with respect to topological equivalence. By Fukuda's cone structure theorem, the topological type of f can be determined by the topological type of its associated link, which is a stable map from S2 to S1. We define a generalized version of the Reeb graph for stable maps γ : S2→ S1, which turns out to be a complete topological invariant. If f has corank 1, then f can be seen as a stabilization of a function h0: (ℝ2, 0) → (ℝ, 0), and we show that the Reeb graph is the sum of the partial trees of the positive and negative stabilizations of h0. Finally, we apply this to give a complete topological description of all map germs with Boardman symbol Σ2, 1.

Fuzzy transition region in a one-dimensional coupled-stable-map lattice

1998 ◽  
Vol 57 (3) ◽  
pp. 2703-2712 ◽  
Author(s):  
F. Cecconi ◽  
R. Livi ◽  
A. Politi
Keyword(s):  
Transition Region ◽  
One Dimensional ◽  
Stable Map
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