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SUMMARY:A couple remarks on parallelism.
DTSTART;VALUE=DATE-TIME:20170624T084500Z
DTEND;VALUE=DATE-TIME:20170624T094500Z
DTSTAMP;VALUE=DATE-TIME:20240527T121213Z
UID:indico-contribution-327-1991@indico.scc.kit.edu
DESCRIPTION:Speakers: Pedro Solórzano ()\nA submetry is a natural general
ization of a riemannian submersion\, which in turn is a natural generaliza
tion of an isometry. We will see how certain properties of riemannian subm
ersions remain valid for submetries provided one is willing to relax their
definitions. In particular\, the notion of parallel translation along arb
itrary paths has a natural generalization. Existence and uniqueness are no
longer guaranteed. Mild assumptions yield existence. Uniqueness\, on th
e other hand\, is harder to subdue. We will discuss natural consequences o
f uniqueness.\n\nhttps://indico.scc.kit.edu/event/327/contributions/1991/
LOCATION:Kollegiengebäude Mathematik (Building 20.30) Seminar Room 1.067
URL:https://indico.scc.kit.edu/event/327/contributions/1991/
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SUMMARY:Alexandrov and Integral Current Spaces (with Jaramillo\, Rajan\, S
earle and Siffert).
DTSTART;VALUE=DATE-TIME:20170624T113000Z
DTEND;VALUE=DATE-TIME:20170624T123000Z
DTSTAMP;VALUE=DATE-TIME:20240527T121213Z
UID:indico-contribution-327-1990@indico.scc.kit.edu
DESCRIPTION:Speakers: Raquel Perales (Instituto de Matemáticas\, UNAM\, M
exico)\nIn this talk we will see that given a closed\, orientable Alexandr
ov space (X\,d) we will define an integral current T defined on X with wei
ght equal to 1 and boundary of T equal to zero. In other words\, this ext
ends to Alexandrov Spaces the canonical current defined on a closed orient
ed Riemannian manifold. We will recall that non collapsing sequences of c
losed oriented compact Riemannian manifolds with a uniform diameter upper
bound and a uniform lower Ricci curvature bound have subsequences that con
verge in both intrinsic flat and Gromov-Hausdorff sense to the same limit
space. Thus\, at the end of the talk we will study the intrinsic flat conv
ergence of sequences of Alexandrov Spaces.\n\nhttps://indico.scc.kit.edu/e
vent/327/contributions/1990/
LOCATION:Kollegiengebäude Mathematik (Building 20.30) Seminar Room 1.067
URL:https://indico.scc.kit.edu/event/327/contributions/1990/
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SUMMARY:On the topology and geometry of higher graph manifold
DTSTART;VALUE=DATE-TIME:20170624T143000Z
DTEND;VALUE=DATE-TIME:20170624T153000Z
DTSTAMP;VALUE=DATE-TIME:20240527T121213Z
UID:indico-contribution-327-1989@indico.scc.kit.edu
DESCRIPTION:Speakers: Pablo Suárez Serrato (Instituto de Matemáticas UNA
M\, Ciudad de México)\nOur understanding of $3$--manifolds has illuminate
d two distinct classes of importance\; hyperbolic manifolds and graphmanif
olds. These are by now considered the basic blocks featured in the geometr
isation program of Thurston\, famously consolidated by Perelman. \n\nFrom
one perspective graph manifolds are exactly the manifolds that {\\it colla
pse}\, in the sense that they admit a family of smooth metrics whose volum
es tend to zero while their sectional curvatures remain bounded. Historica
lly the term {\\it graph manifold} was introduced by Waldhausen in the 196
0's. It highlighted the fact that the fundamental group can be described a
s a graph of groups and that the manifolds were built up from fundamental
pieces that are (heuristically) described in terms of circle bundles over
2-orbifolds. \n\nRecently Frigerio\, Lafont and Sisto proposed a family of
generalised graph manifolds\; products of k--tori with hyperbolic (n-k)--
manifolds with truncated cusps are glued along their common n--toral bound
aries. They explored multiple topological aspects of this family and raise
d some questions. For example\, in their definition k is allowed to equal
zero\, so that one subfamily is made up of hyperbolic manifolds glued alon
g truncated cusps. They asked if the minimal volume of such manifolds is a
chieved by the sum of the hyperbolic volumes of the pieces. \n\nTogether w
ith Chris Connell we answered this question positively. In so doing we rea
lized that a natural family we termed higher graph manifolds could be defi
ned\; bundles of infranilpotent manifolds over negatively curved bases are
glued along boundaries (when possible). This family further extends the o
ne proposed by Frigerio\, Lafont and Sisto. We first characterize the high
er graph manifolds that admit volume collapse\, by explicitly constructing
sequences of metrics of bounded curvature whose volume collapses (this bu
ilds on earlier work by Fukaya). Various results about the simplicial volu
me and volume entropy of this family are calculated. Then we exploit the g
raph structure of the fundamental group to show that these manifolds obey
the coarse Baum-Connes conjecture\, have finite asymptotic dimension and d
o not admit metrics of positive scalar curvature. Finally we use several o
f the produced results to prove that when the infranilmanifold fibre has p
ositive dimension the Yamabe invariant vanishes. \n\nFurther\, in joint wo
rk with Noé Bárcenas and Daniel Juan Pineda we proved that the Borel con
jecture also holds for higher graph manifolds.\n\nhttps://indico.scc.kit.e
du/event/327/contributions/1989/
LOCATION:Kollegiengebäude Mathematik (Building 20.30) Seminar Room 1.067
URL:https://indico.scc.kit.edu/event/327/contributions/1989/
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SUMMARY:Equivariant geometry of Alexandrov 3-spaces.
DTSTART;VALUE=DATE-TIME:20170624T124500Z
DTEND;VALUE=DATE-TIME:20170624T134500Z
DTSTAMP;VALUE=DATE-TIME:20240527T121213Z
UID:indico-contribution-327-1988@indico.scc.kit.edu
DESCRIPTION:Speakers: Jesus Núñez-Zimbrón ((University of California\,
Santa Barbara\, USA)\nAlexandrov spaces constitute a synthetic generalizat
ion of Riemannian manifolds with a lower bound on sectional curvature. The
y provide a natural metric setting to study notions of global Riemannian g
eometry\, and therefore\, a fundamental problem is that of extending to Al
exandrov spaces what is known for Riemannian manifolds. As in the Riemanni
an case\, one may investigate Alexandrov spaces via their symmetries. Sinc
e the isometry group of a compact Alexandrov space is a compact Lie group\
, this point of view naturally leads to the study of isometric Lie group a
ctions on Alexandrov spaces. In this context\, a natural measure of the co
mplexity of an action is the cohomogeneity\, i.e. the dimension of the orb
it space. Berestovskii showed that finite-dimensional homogeneous Alexandr
ov spaces actually are Riemannian manifolds. Galaz-Garcia and Searle studi
ed Alexandrov spaces of cohomogeneity 1 and classified them in dimensions
at most 4.\n\nIn this talk I will present an equivariant and topological c
lassification of closed Alexandrov spaces of dimension 3 admitting isometr
ic actions of cohomogeneity 2 as well as a generalization to the case of i
sometric local circle actions. As an application of this result I will tal
k about some aspects of the geometry (in the sense of Thurston) of Alexand
rov 3-spaces. The results presented here are joint work with Fernando Gala
z-García and Luis Guijarro.\n\nhttps://indico.scc.kit.edu/event/327/contr
ibutions/1988/
LOCATION:Kollegiengebäude Mathematik (Building 20.30) Seminar Room 1.067
URL:https://indico.scc.kit.edu/event/327/contributions/1988/
END:VEVENT
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SUMMARY:Geometry of null hypersurfaces
DTSTART;VALUE=DATE-TIME:20170624T073000Z
DTEND;VALUE=DATE-TIME:20170624T083000Z
DTSTAMP;VALUE=DATE-TIME:20240527T121213Z
UID:indico-contribution-327-1987@indico.scc.kit.edu
DESCRIPTION:Speakers: Oscar Palmas (Facultad de Ciencias\, UNAM\, Mexico)\
nGiven a semi-Riemannian manifold $\\bar M$ with metric $\\bar g$\, a subm
anifold $M$ of $\\bar M$ is null if the restriction $g$ of $\\bar g$ to $M
$ is degenerate. These objects deserve some attention\, because of their c
onnection with some areas like the study of black holes and others. In gen
eral\, some properties of $M$ cannot be studied with the usual differentia
l geometric methods\, but here we discuss the case of null hypersurfaces i
n Lorentzian space forms. This is a joint work with M. Navarro and D. Soli
s (UADY-Mexico)\n\nhttps://indico.scc.kit.edu/event/327/contributions/1987
/
LOCATION:Kollegiengebäude Mathematik (Building 20.30) Seminar Room 1.067
URL:https://indico.scc.kit.edu/event/327/contributions/1987/
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