Related papers: The topological Singer construction

Observation of top quark flavor changing neutral process $t\to c +\gamma$ at the LHC would be the signal of physics beyond the Standard Model. If anomalous $t\to c\gamma$ coupling exists, it will affect the precisely measured…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

The homotopy theory of the blow up construction in algebraic and symplectic geometry is investigated via two approaches. The first approach introduces and develops fibrewise surgery theory, for which the fibrewise framing is characterized…

Let Gamma be a semidirect product of the form Z^n rtimes Z/p where p is prime and the Z/p-action on Z^n is free away from the origin. We will compute the topological K-theory of the real and complex group C*-algebra of Gamma and show that…

Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases,…

The analysis of ``tangent maps'' at singular points of energy minimizing maps plays an important role in our understanding of the fine structure of the singular set. This note presents the first example of a minimizing (not just stationary)…

If $B$ is a toric manifold and $E$ is a Whitney sum of complex line bundles over $B$, then the projectivization $P(E)$ of $E$ is again a toric manifold. Starting with $B$ as a point and repeating this construction, we obtain a sequence of…

Let $\mathcal{P}_G$ be the family of all topologically mixing, but not exact self-maps of a topological graph $G$. It is proved that the infimum of topological entropies of maps from $\mathcal{P}_G$ is bounded from below by $(\log 3/…

This paper studies the integral cohomology ring of the classifying space $BPU_n$ of the projective unitary group $PU_n$. By calculating a Serre spectral sequence, we determine the ring stucture of $H^*(BPU_n;\mathbb{Z})$ in dimensions $\leq…

We calculate the mod (p, v_1, v_2) homotopy V(2)_* TC(BP<2>) of the topological cyclic homology of the truncated Brown--Peterson spectrum BP<2>, at all primes p\ge7, and show that it is a finitely generated and free F_p[v_3]-module on 12p+4…

In this note we show that a $p$-complete nilpotent space $X$ has a $p$-complete suspension spectrum if and only if its homotopy groups $\pi_*X$ are bounded $p$-torsion. In contrast, if $\pi_*X$ is not all bounded $p$-torsion, we locate…

We study the $p$-spectrum of a locally symmetric space of constant curvature $\Gamma\backslash X$, in connection with the right regular representation of the full isometry group $G$ of $X$ on $L^2(\Gamma\backslash G)_{\tau_p}$, where…

For finite dimensional free $C_p$-spaces, the calculation of the Bredon cohomology ring as an algebra over the cohomology of $S^0$ is used to prove the non-existence of certain $C_p$-maps. These are related to Borsuk-Ulam type theorems, and…

Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables…

We provide a general method computing the mod $p$ Quillen homology of algebras over a monad that parametrizes the structure of mod $p$ homology of spectral Lie algebras. This is the $E^2$-page of the bar spectral sequence converging to the…

We prove a necessary condition for the existence of the $A_p$-structure on ${\rm mod}~p$ spaces, and also derive a simple proof for the finiteness of the number of ${\rm mod}~p$ $A_p$-spaces of given rank. As a direct application, we…

In the first part of this paper, we constructed a filtered U(r)-equivariant stable homotopy type called the spectrum of strict broken symmetries sB(L) of links L given by closing a braid with r strands. Evaluating this filtered spectrum on…

We investigate topological phases in two-dimensional Bi/Sb honeycomb crystals considering planar, buckled, freestanding and deposited on a substrate structures. We use the multi-orbital tight-binding model and compare results with density…

The completion tower of a nonunital commutative ring is a classical construction in commutative algebra. In the setting of structured ring spectra as modeled by algebras over a spectral operad, the analogous construction is the homotopy…

Fix an odd prime $p$. Let $X$ be a pointed space whose $p$-completed K-theory $\mathrm{KU}_p^*(X)$ is an exterior algebra on a finite number of odd generators; examples include odd spheres and many H-spaces. We give a…