arXiv subjects
Publications and source records attributed to J Morava.
The principal result of this note is the existence of a complex topological orientation for Atiyah-Segal $\mathbb{T}$-equivariant K-theory which indexes the projective space of lines in complex (n+1)-space by the Fourier expansion $1 + q + \dots + q^n$.
We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$ - bundles ($\S2$, generalizing contact structures). Powerful $sl_2$ - representation-valued Hodge-Lefschetz cohomology (going back to Chern and Weil), taking values in the $\mathbb{Z}$-graded category of bidifferential modules of Angella, Otiman, and Tardini is available for its study. This is an extended revision with a detailed introduction replacing the final section. The original concern of the paper was a characteristic two issue which remains unchanged.
The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat connection on that bundle, regarded as defined over a thickening of $X$ by an infinitesimal disk. The theory of Fourier integral operators on manifolds reconciles dimensional and zeta-function regularization by interpreting this disk as the germ of a neighborhood of a Jordan curve around $\infty$ on the Riemann sphere. Such fields $X \to \Omega S^2$ were proposed in \cite{14} as useful in these contexts.
We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology $t_\T E$ of a complex-oriented $E_\infty$ ring-spectrum $E$ is the extension of a Hopf algebra by its dual, which provides an algebraic rigidification of geometric interest. This note reviews the cases $E = H,K$ and $MU$, with special attention to $\lambda$-ring structures.