Related papers: Homotopy string links and the $\kappa$-invariant

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…

In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal, Costello, and Hopkins and Lurie, on "open-closed topological conformal field theories". Given a…

A polynomial knot in $\mathbb{R}^n$ is a smooth embedding of $\mathbb{R}$ in $\mathbb{R}^n$ such that the component functions are real polynomials. In the earlier paper with Mishra, we have studied the space $\mathcal{P}$ of polynomial…

We construct an algebraic model for the Chas-Sullivan product and the Goresky-Hingston coproduct in string topology. The construction takes as its initial input a simplicial complex equipped with a local pairing on its simplicial chains,…

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…

Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine…

We propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the $p$-local integers. For the tamely ramified extension of…

Given a closed manifold $M$. We give an algebraic model for the Chas-Sullivan product and the Goresky-Hingston coproduct. In the simply-connected case, this admits a particularly nice description in terms of a Poincar\'e duality model of…

Cosmic strings in the early universe have received revived interest in recent years. In this paper we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…

For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k-tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we require…

Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular…

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map from a topological manifold M to another N naturally induces a map from the structure set S(M) to S(N). We extend…

This paper presents some basic facts about the so-called connectivity spaces. In particular, it studies the generation of connectivity structures, the existence of limits and colimits in the main categories of connectivity spaces, the…

A thick link is a link in $\mathbb{R}^3$ such that each component of the link lies at distance at least $1$ from every other component. Strengthening the notion of thickness, we define a thickly embedded link to be a thick link whose open…

In previous work, the first author defined homotopy theories for stratified spaces from a simplicial and a topological perspective. In both frameworks stratified weak-equivalences are detected by suitable generalizations of homotopy links.…

We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the $m$ dimensional real projective space into the $n$ dimensional complex projective space for $2\leq m\leq 2n$ (we conjecture…

In this paper, the knotlike cosmic strings in the Riemann-Cartan space-time of the early universe are discussed. It has been revealed that the cosmic strings can just originate from the zero points of the complex scalar quintessence field.…

Given a map $f: X\rightarrow Y$ of simply connected spaces of finite type such. The space of based loops at $f$ of the space of maps between $X$ and $Y$ is denoted by $\Omega_{f} Map(X,Y)$. For $n> 0$, we give a model categorical…

Fix an integer N>1. To each diagram of a link colored by 1,...,N, we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every…