Related papers: A negative answer to the problem: are stratifiable…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together…
In this note we present examples of localization functors (in the category of spaces) whose composition with certain cellularization functors is not idempotent, and vice versa.
Localized noncommutative structures for manifolds with connection are constructed based on the use of vertical star products. The model's main feature is that two points that are far away from each other will not be subject to a deviation…
This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is $L$-selective but not $\mathbb{Q}$-selective…
The mu-invariant mu = (\mu_1,\mu_2,\mu_3) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same mu-type, what we call a mu-stratum, and as…
In [1] we introduced the notion of 'structured space', i.e. a space which locally resembles various algebraic structures. In [2] and [3] we studied some cohomology theories related to these space. In this paper we continue in this…
We define a class of trim metric spaces and show that every finite metric space is the leaf space of a metric forest with trim base.
We construct oriented matroids of rank 3 on 13 points whose realization spaces are disconnected. They are defined on smaller points than the known examples with this property. Moreover, we construct the one on 13 points whose realization…
This paper contains some results about the topology of $\M_{0,n+1}/\Sigma_n$, where $\M_{0,n+1}$ is the moduli space of genus zero Riemann surfaces with marked points. We show that $\M_{0,n+1}/\Sigma_n$ is not a topological manifold for…
Consider the moduli space M^0 of arrangements of n hyperplanes in general position in projective (r-1)-space. When r=2 the space has a compactification given by the moduli space of stable curves of genus 0 with n marked points. In higher…
We study moduli spaces $M_X(r,c_1,c_2)$ parametrizing slope semistable vector bundles of rank $r$ and fixed Chern classes $c_1, c_2$ on a ruled surface whose base is a rational nodal curve. We show that under certain conditions, these…
Recently Ott, Tomforde and Willis proposed a new approach for one sided shift spaces over infinite alphabets. In this new approach the conjugacy classes of shifts of finite type, edge shifts, and M-step shifts are distinct and the authors…
There are various statements in the physics literature about the stratification of quantum states, for example into orbits of a unitary group, and about generalized differentiable structures on it. Our aim is to clarify and make precise…
In this paper we study monomial multiple structures on a linear subspace of codimension two in projective space. We show that these structures determine smooth points in their respective Hilbert schemes, with (smooth) neighbourhoods of two…
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…
Withdrawn paper because the results are recycled in several other papers and a new definition of T-homotopy is proposed in math.AT/0505152.
In this paper we construct various non-trivial and non-tautological cohomology classes on compactified and uncompactified strata of curves with a differential, by using the geometry of the boundary stratification of the moduli space of…
If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if…
The first results, both positive and negative, recently obtained in the area of constructing stationary spinning solitons in flat Minkowski space in 3+1 dimensions are discussed.