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On immersions of uncountable graphs

2003
*
Journal of combinatorial theory. Series B (Print)
*

Soc. 61 (1965) 697), Nash-Williams proposed the conjecture that the class

doi:10.1016/s0095-8956(02)00030-8
fatcat:hbvytdmbazh5pkzfxl7pso6s7e
*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: ...##
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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 ...##
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Orientations of infinite graphs with prescribed edge-connectivity

2015
*
Combinatorica
*

It implies that every 4k-edge-connected

doi:10.1007/s00493-015-3173-0
fatcat:3zuvgkhybzb37hgs3lqj4mwl5e
*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. ...##
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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. ...##
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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 ...##
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Exotic smoothings via large ℝ4's in Stein surfaces

2016
*
Algebraic and Geometric Topology
*

This relies

doi:10.2140/agt.2016.16.1637
fatcat:qhtqhsf5kfgijke5zxwdfbq544
*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. ...##
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On the non-existence of solutions of the Dirichlet problem for the minimal surface system
[article]

2020
*
arXiv
*
pre-print

We generalize Lawson-Osserman's result

arXiv:1812.11553v5
fatcat:cphic5ij4zazharyphjktznmpm
*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. ...##
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Perfect domination in regular grid graphs
[article]

2010
*
arXiv
*
pre-print

We show there is an

arXiv:0711.4343v4
fatcat:zpxxtouptjf6hmxmk2xjogeqie
*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 ...##
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Learning about Reality from Observation

2003
*
SIAM Journal on Applied Dynamical Systems
*

When can we say that A and φ(A) are similar, based only

doi:10.1137/s1111111102407421
fatcat:x3skdmrbljenbjgbmbfxc5i35i
*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. ...##
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Crystallography and Riemann Surfaces
[article]

1999
*
arXiv
*
pre-print

To obtain a wider spectrum

arXiv:math/9904016v1
fatcat:lp2dop3bqbamnnhxnxx523ghay
*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. ...##
###
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.) ...##
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Algebraic intermediate hyperbolicities
[article]

2021
*
arXiv
*
pre-print

Our work answers the algebraic analogue

arXiv:2012.07803v2
fatcat:udgvp7nmcrb7hamdbz6c2h64tq
*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]. ...##
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On convexity of hypersurfaces in the hyperbolic space

2008
*
Geometriae Dedicata
*

In the Hyperbolic space H n (n ≥ 3) there are

doi:10.1007/s10711-008-9278-5
fatcat:j2dnqfwl7zdrzodnk3v562vr2a
*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). ...##
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An interesting class of C1 foliations

2002
*
Topology and its Applications
*

There result

doi:10.1016/s0166-8641(02)00089-5
fatcat:j7mrlnkdo5hnzfxddoerhgqfmu
*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. ...##
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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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