Related papers: Coproducts in brane topology

We study the $E_2$-algebra $\Lambda\mathfrak{M}_{*,1}=\coprod_{g\geqslant 0}\Lambda\mathfrak{M}_{g,1}$ consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised boundary component, and compute the homotopy…

A result of B.Solomon (On the Gauss map of an area-minimizing hypersurface. 1984. Journal of Differential Geometry, 19(1), 221-232.) says that a compact minimal hypersurface $M^k$ of the sphere $S^{k+1}$ with $H^1(M)=0$, whose Gauss map…

The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the…

The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of…

In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a…

We study the cosmological evolution of extended branes in 6D warped flux compactification models. The branes are endowed with the three ordinary spatial dimensions, which are assumed to be homogeneous and isotropic, as well as an internal…

Open branes ending on other branes, which may be referred to as the host branes, are studied in the superembedding formalism. The open brane, host brane and the target space in which they are both embedded are all taken to be…

We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M. We also prove related results…

We prove that an embedded cobordism between manifolds with boundary can be split into a sequence of right product and left product cobordisms, if the codimension of the embedding is at least two. This is a topological counterpart of the…

N=1 supersymmetric QCD is considered using the recently proposed picture of it as the world volume theory of a single M-theory fivebrane with two of its dimensions wrapped on a Riemann surface. The conditions under which a second M-theory…

Our main result is a generalization of Cappell's 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For…

`Loop-fusion cohomology' is defined on the continuous loop space of a manifold in terms of \vCech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that…

In this paper, we introduce coproducts of proximity spaces. After exploring several of their basic properties, we show that given a collection of proximity spaces, the coproduct of their Smirnov compactifications proximally and densely…

The loop product is an operation in string topology. Cohen and Jones gave a homotopy theoretic realization of the loop product as a classical ring spectrum $LM^{-TM}$ for a manifold $M$. Using this, they presented a proof of the statement…

We calculate mod-p cohomology of extended powers, and their group completions which are free infinite loop spaces. We consider the cohomology of all extended powers of a space together and identify a Hopf ring structure with divided powers…

Let F_*(X, Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form X cup_{alpha}e^{k+1} and a space Y whose connectivity exceeds the dimension of the…

Let K denote a field. Given an arbitrary linear subspace V of M_n(K) of codimension lesser than n-1, a classical result states that V generates the K-algebra M_n(K). Here, we strengthen this in three ways: we show that M_n(K) is spanned by…

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…

We endow the cohomology of configuration spaces of a manifold with a product arising from superposing configurations. We prove that, under the scanning isomorphism, this product corresponds to the cup-product of the section space of the…

We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded…