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On immersions of uncountable graphs

Thomas Andreae
2003 Journal of combinatorial theory. Series B (Print)  
Soc. 61 (1965) 697), Nash-Williams proposed the conjecture that the class of all graphs (finite or infinite) is well-quasi-ordered by the immersion relation (which is denoted here by p 1 ).  ...  In his paper on well-quasi-ordering infinite trees (Proc. Cambridge Philos.  ...  H 0 1 ; H 0 2 ; y of uncountable graphs such that H 0 i 4 / 2 H 0 j for all positive integers i; j with iaj:  ... 
doi:10.1016/s0095-8956(02)00030-8 fatcat:hbvytdmbazh5pkzfxl7pso6s7e

Page 8797 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
Summary: “Recent results on the immersion relation for graphs are applied to show that there exist (uncountable) graphs A and G such that G contains n disjoint copies of A for each positive integer n,  ...  trees and (ii) graphs for which adding some / edges produces a graph which is decomposable into k spanning trees.” 2002m:05060 05C10 Andreae, Thomas (D-HAMB-SM; Hamburg) On the immersion relation and  ... 

Orientations of infinite graphs with prescribed edge-connectivity

Carsten Thomassen
2015 Combinatorica  
It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex set (while planar graphs show that G need not contain  ...  a subdivision of a simple finite graph of large edge-connectivity).  ...  Acknowledgement Thanks are due to a referee for having detected an error the the original version of Theorem 1 which lead to the present version.  ... 
doi:10.1007/s00493-015-3173-0 fatcat:3zuvgkhybzb37hgs3lqj4mwl5e

Page 1026 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
product of such a 3-manifold with R, admits uncountably many smooth structures.  ...  The estimate of the unknotting number is given in terms of vertices of charts cor- responding to double points of immersions and triple points of their projections.  ... 

Page 1729 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
(D-HAMB-SM; Hamburg) On immersions of uncountable graphs.  ...  By definition H <, G if there exists an immersion from H to G, that is, a function y which maps V (H) one-to-one into V(G), maps edges xy to nontrivial paths in G with terminal vertices (x), p(y), and  ... 

Exotic smoothings via large ℝ4's in Stein surfaces

Julia Bennett
2016 Algebraic and Geometric Topology  
This relies on an extension of Casson's Embedding Theorem for locating Casson handles in closed 4-manifolds.  ...  In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces.  ...  Define G to be the graph obtained by removing all loops from the graph corresponding to this configuration of spheres.  ... 
doi:10.2140/agt.2016.16.1637 fatcat:qhtqhsf5kfgijke5zxwdfbq544

On the non-existence of solutions of the Dirichlet problem for the minimal surface system [article]

Yongsheng Zhang
2020 arXiv   pre-print
We generalize Lawson-Osserman's result on the non-existence of solutions to the Dirichlet problem for minimal graphs of codimension ≥ 2.  ...  Instead of an attempt on a direct application of Theorem 1.2, we alter the argument to fit boundary LOMSEs. Even if ι is not a covering, it is always an immersion.  ...  Locally ι is an embedding and one can pull back the normal bundle of the immersed submanifold to P . Let N be the pull-back bundle and ǫ 0 the normal radius of first focal point.  ... 
arXiv:1812.11553v5 fatcat:cphic5ij4zazharyphjktznmpm

Perfect domination in regular grid graphs [article]

Italo J. Dejter
2010 arXiv   pre-print
We show there is an uncountable number of parallel total perfect codes in the integer lattice graph Λ of ^2.  ...  In contrast, there is just one 1-perfect code in Λ and one total perfect code in Λ restricting to total perfect codes of rectangular grid graphs (yielding an asymmetric, Penrose, tiling of the plane).  ...  In contrast with the mentioned uncountability, seen as one of perfect dominating sets, not only there is just one 1-perfect code in Λ but, as a result of a characterization of grid graphs containing total  ... 
arXiv:0711.4343v4 fatcat:zpxxtouptjf6hmxmk2xjogeqie

Learning about Reality from Observation

William Ott, James A. Yorke
2003 SIAM Journal on Applied Dynamical Systems  
When can we say that A and φ(A) are similar, based only on knowledge of the images in R m of trajectories in A?  ...  Let A be a compact invariant set for a map f on R n and let φ : R n → R m where n > m be a "typical" smooth map.  ...  Michael Brin for his numerous insightful comments on a draft.  ... 
doi:10.1137/s1111111102407421 fatcat:x3skdmrbljenbjgbmbfxc5i35i

Crystallography and Riemann Surfaces [article]

Veit Elser
1999 arXiv   pre-print
To obtain a wider spectrum of point sets, we consider, more generally, a Riemann surface S immersed in C^2 and its sections ("cuts") by C.  ...  Our main result concerns the special case of maps of right triangles, with the right angle being a regular point of the map.  ...  Acknowledgements I thank the Aspen Center for Physics, where a large part of this paper was written. Noam Elkies provided a useful suggestion for the proof of Lemma 2.12.  ... 
arXiv:math/9904016v1 fatcat:lp2dop3bqbamnnhxnxx523ghay

Page 3381 of Mathematical Reviews Vol. , Issue 88g [page]

1988 Mathematical Reviews  
The main result, established by exhibiting a suitable immersion between the relevant quasi-orders, is that the graph minor theorem, restricted to graphs of bounded tree-width, implies (in the weak base  ...  (Before dismissing this gener- alization as unimportant one should note that the natural way to describe a real vector space is as an abelian group with uncount- ably many operators.)  ... 

Algebraic intermediate hyperbolicities [article]

Antoine Etesse and Ariyan Javanpeykar and Erwan Rousseau
2021 arXiv   pre-print
Our work answers the algebraic analogue of a question of Kobayashi on analytic hyperbolicity.  ...  Then, we prove that this intermediate algebraic hyperbolicity implies the finiteness of the group of birational automorphisms and of the set of surjective maps from a given projective variety.  ...  If Hilb(Y × X) is the Hilbert scheme of Y × X, then the morphism Hom(Y, X) → Hilb(Y × X) mapping a morphism f : Y → X to its graph Graph(f ) ⊂ Y × X is an open immersion [Nit05, Theorem 6.6].  ... 
arXiv:2012.07803v2 fatcat:udgvp7nmcrb7hamdbz6c2h64tq

On convexity of hypersurfaces in the hyperbolic space

Konstantin Rybnikov
2008 Geometriae Dedicata  
In the Hyperbolic space H n (n ≥ 3) there are uncountably many topological types of convex hypersurfaces.  ...  We prove that any locally convex proper embedding of an (n − 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n − 1)-flats of the resulting hypersurface is  ...  The graph of the resulting function looks like a hat. Consider this graph as an embedded surface in the hyperbolic space (Beltrami-Klein model).  ... 
doi:10.1007/s10711-008-9278-5 fatcat:j2dnqfwl7zdrzodnk3v562vr2a

An interesting class of C1 foliations

John Cantwell, Lawrence Conlon
2002 Topology and its Applications  
There result uncountably many examples of C 1 foliations that are not homeomorphic to C 2 foliations, as well as uncountably many C 0 foliations that are not homeomorphic to C 1 foliations. : S 0 1 6 6  ...  -8 6 4 1 ( 0 2 ) 0 0 0 8 9 -5 The fundamental intervals In order to define f and g, we determine the intervals I p,q that were the vertices of the graph Γ in Section 3.  ...  As in Section 3, the graph is immersed in R 2 so that its vertices I p,q are the points (p, q) of the integer lattice.  ... 
doi:10.1016/s0166-8641(02)00089-5 fatcat:j7mrlnkdo5hnzfxddoerhgqfmu

Page 3408 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Martinez [Antonio Martinez], On the second fundamental form of an immersion in a quaternion Kahler manifold (Spanish) (pp. 59-66); M.  ...  Hernandez, A note on the B-convexity of weighted Orlicz sequence spaces (pp. 392-396); Antonio Sudrez Granero, Some uncountable structures and the Choquet - Edgar property in nonseparable Banach spaces  ... 
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