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The minimal genus problem for elliptic surfaces
4-manifold elliptic surface diffeomorphism group minimal genus
2012/6/25
We partly solve the minimal genus problem for embedded surfaces in the case of elliptic 4-manifolds. This involves a certain restricted transitivity property of the action of the orientation preservin...
Skeletally Dugundji spaces
absolute Dugundji spaces inverse system open maps skeletally Dugundji spaces skeletal maps
2012/6/21
We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. The main result states that the following conditions are equivalent for a given space $X$...
Unknotting numbers and triple point cancelling numbers of torus-covering knots
Surface knot 2-dimensional braid quandle cocycle invariant unknotting number triple point cancelling number
2012/6/21
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum numb...
Visual limits of maximal flats in symmetric spaces and Euclidean buildings
visual limit geometric limit CAT(0) geometry geodesic boundary convex subset maximal flat symmetric space of non-compact type Euclidean building topological spherical building
2012/6/25
Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal...
Homomorphisms between diffeomorphism groups
Homomorphisms diffeomorphism groups Geometric Topology
2012/6/25
For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial ...
Multidimensional Interleavings and Applications to Topological Inference
Multidimensional Interleavings Topological Inference Algebraic Topology
2012/6/27
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at t...
In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually in...
Asymptotic formulas for curve operators in TQFT
Asymptotic formulas curve operators TQFT Geometric Topology
2012/6/21
Topological quantum field theories with gauge group $\textrm{SU}_2$ associate to each surface with marked points $\Sigma$ and each integer $r>0$ a vector space $V_r (\Sigma)$ and to each simple closed...
A space is od-compact (resp. od-Lindel\"of) provided any cover by open dense sets has a finite (resp. countable) subcover. We first show with simple examples that these properties behave quite poorly ...
Symmetric Squaring in Homology and Bordism
algebraic topology homology theory bordism Cech homology
2012/6/19
Looking at the cartesian product X \times X of a topological space X with itself, a natural map to be considered on that object is the involution that interchanges the coordinates, i.e. that maps (x, ...
This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C. The techniques currently available in the literature are either too t...
On character of points in the Higson corona of a metric space
Higson corona character of a point ultrafilter number dominating number
2012/6/19
We prove that for an unbounded metric space $X$, the minimal character $m\chi(\check X)$ of a point of the Higson corona $\check X$ of $X$ is equal to $\mathfrak u$ if $X$ has asymptotically isolated ...
Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known.
Topological graph clustering with thin position
Thin position data mining graph partitioning
2012/6/21
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data...
Funar algebra $K_\infty=K_\infty(\alpha,\beta;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $\sigma_1^3-\alpha\sigma_1^2+\beta\sigma_1-...