相关论文: On the invariance of the string topology coproduct

Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…

We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this…

Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain…

String propagation on a cone with deficit angle $2\pi (1- \frac{1}{N} ) $ is described by constructing a non-compact orbifold of a plane by a $Z_{N}$ subgroup of rotations. It is modular invariant and has tachyons in the twisted sectors…

I construct a complete 1-loop partition function of a bosonic closed string on orbifolds. Furthermore, I derive sufficient conditions for the modular invariance of the partition function.

We prove that on 2-connected closed oriented manifolds, the analytic and algebraic constructions of an IBL$_\infty$ structure associated to a closed oriented manifold coincide. The corresponding structure is invariant under orientation…

We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…

We prove the Gap Theorem for the spectrum of topological modular forms $\mathrm{Tmf}$. This removes a longstanding circularity in the literature, thereby confirming the computation of $\pi_\ast \mathrm{tmf}$ from over two decades ago by…

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or…

We give a complete obstruction to turning an immersion of an m-dimensional manifold M in Euclidean n-space into an embedding when 3n>4m+4. It is a secondary obstruction, and exists only when the primary obstruction, due to Haefliger,…

We examine the structure of higher-derivative string corrections under a cosmological reduction and make connection to generalized geometry and T-duality. We observe that, while the curvature $R^\mu{}_{\nu\rho\sigma}(\Omega_+)$ of the…

Heaps' or Herdan's law characterizes the word-type vs. word-token relation by a power-law function, which is concave in linear-linear scale but a straight line in log-log scale. However, it has been observed that even in log-log scale, the…

We prove a result of equivalence invariance of formal category theory for statements that can be expressed within an equipment. To do this, we exploit Henry and Bardomiano Mart\'inez's link between Makkai's FOLDS (first order logic with…

We consider vacuum tunneling of a new kind where the false vacua are not translationally invariant, but have topological defects that break some of their translational symmetries. In the particular case where the topological defects are…

We point out that the celebrated Hawking effect of quantum instability of black holes seems to be related to a nonperturbative effect in string theory. Studying quantum dynamics of strings in the gravitational background of black holes we…

This note discusses some geometrically defined seminorms on the group $\Ham(M, \omega)$ of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M, \omega)$, giving conditions under which they are nondegenerate and explaining their…

In the paper we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an…

We show that, in string theory, as a result of the $W_{\infty}$-symmetries that preserve quantum coherence in the {\it full} string theory by coupling different mass levels, transitions between initial- and final-state density matrices for…