arXiv subjects

M. J. Hopkins

Publications and source records attributed to M. J. Hopkins.

4 recordsLinked to original sources

arXiv2005

Quadratic functions in geometry, topology,and M-theory

We describe an interpretation of the Kervaire invariant of a Riemannian manifold of dimension $4k+2$ in terms of a holomorphic line bundle on the abelian variety $H^{2k+1}(M)\otimes R/Z$. Our results are inspired by work of Witten on the fivebrane partition function in $M$-theory (hep-th/9610234, hep-th/9609122). Our construction requires a refinement of the algebraic topology of smooth manifolds better suited to the needs of mathematical physics, and is based on our theory of "differential functions." These differential functions generalize the differential characters of Cheeger-Simons, and the bulk of this paper is devoted to their study.

math.AT↗

arXiv2000

On Ramond-Ramond fields and K-theory

A recent paper by Moore and Witten explained that Ramond-Ramond fields in Type II superstring theory have a global meaning in K-theory. In this note we amplify and generalize some points raised in that paper. In particular, we express the coupling of the Ramond-Ramond fields to D-branes in a K-theoretic framework and show that the anomaly in this coupling exactly cancels the anomaly from the fermions on the brane, both in Type IIA and Type IIB.

hep-th↗

arXiv1999

Vanishing lines in generalized Adams spectral sequences are generic

We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.

math.AT↗

arXiv1998

Vanishing lines in Adams spectral sequences are generic

We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.

math.AT↗