Related papers: KSp-characteristic classes determine Spin$^h$ cobo…

We have proposed a fully quantum approach to non-perturbatively calculate the spin-split Landau levels and g-factor of various spin-orbit coupled solids, based on the k.p theory in the matrix mechanics representation. The new method…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{odd-form} symmetries determined by $K_N(\partial X)$, the twisted K-theory as D-brane charges on the…

We compute the algebraic $K$-theory of some classes of surfaces defined over finite fields. We achieve this by first calculating the motivic cohomology groups and then studying the motivic Atiyah-Hirzebruch spectral sequence. In an…

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E_2-term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a…

We study M-theory on two classes of manifolds of Spin(7) holonomy that are developing an isolated conical singularity. We construct explicitly a new class of Spin(7) manifolds and analyse in detail the topology of the corresponding…

We consider the role of the Kervaire--Milnor invariant in the classification of closed, connected, spin 4-manifolds, typically denoted by $M$, up to stabilisation by connected sums with copies of $S^2 \times S^2$. This stable classification…

We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…

Any bounding compact smooth manifold bounds a compact manifold with a spine consisting of transversely intersecting codimension one submanifolds. This paper provides details for a picture proof given in previous papers with S. Akbulut.

We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 with H^3(M; \Q) = 0 such that c_2(E)\in H^4(M) is torsion. The…

We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a…

Let $\mathfrak{G}=\mathfrak{S}_{q} \overleftrightarrow{\times} \mathfrak{S}_q$ be the $\mathbb{Z}/2$-extension of the product of two symmetric groups $\mathfrak{S}_{q} \times \mathfrak{S}_q$. In this paper, we compute the…

We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the…

Let $SL_{2n}$, $Sp_{2n}$, $E_6 = G^{sc}(E_6)$, $F_4 = G(F_4)$ be simply connected split algebraic groups over an arbitrary field $F$. Algebraic K-theory of affine homogeneous varieties $SL_{2n}/Sp_{2n}$ and $E_6/F_4$ is computed. Moreover,…

Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $\theta(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the…

It is shown that every bundle $\varSigma\to M$ of complex spinor modules over the Clifford bundle $\Cl(g)$ of a Riemannian space $(M,g)$ with local model $(V,h)$ is associated with an lpin ("Lipschitz") structure on $M$, this being a…

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…

In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The $\mathcal{N}=1$ superconformal algebra is extended by additional generators of…

The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples S//p for prime numbers p. These can be realized as Thom spectra, and therefore relate to other Thom spectra such as…