Related papers: String Topology, Euler Class and TNCZ free loop fi…

We study string topology for classifying spaces of connected compact Lie groups, drawing connections with Hochschild cohomology and equivariant homotopy theory. First, for a compact Lie group $G$, we show that the string topology…

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

We study topology in gapless phases of an interacting spinful model with spin-charge separation. We focus on the gapless boundaries between $\mathbb{Z}_2$ symmetry-breaking phases. We find two topologically non-trivial gapless states that…

In this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain…

We prove that any topological loop homeomorphic to a sphere or to a real projective space and having a compact-free Lie group as the inner mapping group is homeomorphic to the circle. Moreover, we classify the differentiable $1$-dimensional…

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 positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M,\Lambda)$…

We provide an explicit computation over the integers of the bar version $\overline{HM}_*$ of the monopole Floer homology of a three-manifold in terms of a new invariant associated to its triple cup product called extended cup homology. This…

Let $g$ be a non-negative integer, $\Sigma _g$ a closed orientable surface of genus $g$, and $\mathcal{M}_g$ its mapping class group. We classify all the group homomorphisms $\pi _1(\Sigma _g)\to G$ up to the action of $\mathcal{M}_g$ on…

Given an action $G \curvearrowright X$ of a discrete and countable infinite group $G$ on a compact and Hausdorff space $X$, we regard $\ell^1(G\curvearrowright X)$ as the Banach *-algebra crossed product associated to the action. We…

This paper studies the question of when a loop $\phi$ in the group Symp$(M,\omega)$ of symplectomorphisms of a symplectic manifold $(M,\omega)$ is isotopic to a loop that is generated by a time-dependent Hamiltonian function. (Loops with…

We decompose the twisted index obstruction $\theta(M)$ against positive scalar curvature metrics for oriented manifolds with spin universal cover into a pairing of a twisted $K$-homology with a twisted $K$-theory class and prove that…

Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group $F(X)$ over a Tychonov space $X$ is $o$-bounded if and only if every continuous metrizable image $T$ of $X$ satisfies the selection…

The string topology coproduct is often perceived as a counterpart in string topology to the Chas-Sullivan product. However, in certain aspects the string topology coproduct is much harder to understand than the Chas-Sullivan product. In…

We prove that if the $f$-sectional curvature at any point $p$ of a $(2n+s)$-dimensional $f$-$(\kappa,\mu)$ manifold with $n>1$ is independent of the $f$-section at $p$, then it is constant on the manifold. Moreover, we also prove that an…

Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting $k$ independent closed one-forms fibers over a torus $T^k$. In this article we explain a version of this…

We study the holomorphic vector bundles E over the twistor space Tw(M) of a compact simply connected hyperk\"ahler manifold $M$. We give a characterization of the semistability condition for E in terms of its restrictions to the holomorphic…

A topological group $G$ is called an $M_\omega$-group if it admits a countable cover $\K$ by closed metrizable subspaces of $G$ such that a subset $U$ of $G$ is open in $G$ if and only if $U\cap K$ is open in $K$ for every $K\in\K$. It is…

Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant {\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2) then M is of…

Given a simply connected manifold M such that its cochain algebra, C^\star(M), is a pure Sullivan dga, this paper considers curved deformations of the algebra C_\star({\Omega}M) and consider when the category of curved modules over these…