The second edition builds on the first in several ways. There are three new chapters which
survey recent directions and extensions of the theory, and there are two new appendices …

A bstract The three tachyon-free non-supersymmetric string theories in ten dimensions
provide a handle on quantum gravity away from the supersymmetric lamppost. However …

Quadratic refinements of the intersection pairing on a Riemann surface appear to have two
mathematical origins: one in complex function theory dating back to Riemann in the 1870's …

A bstract The landscape of six-dimensional supergravities is dramatically constrained by the
cancellation of gauge and gravitational anomalies, but the full extent of its implications has …

This paper is part of a series ([HMM98, HM98] and other work in progress) getting at some
new aspects of the topological approach to elliptic genera. Most of these results were …

The connective topological modular forms spectrum, $ tmf $, is in a sense initial among
elliptic spectra, and as such is an important link between the homotopy groups of spheres …

Modular forms appear in many facets of mathematics, and have played important roles in
geometry, mathematical physics, number theory, representation theory, topology, and other …

We provide a model of the String group as a central extension of finite-dimensional 2–
groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This …

To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

In [2; 3; 4], Hopkins, Mahowald, and Miller constructed a new homology theory called tmf, or
topological modular forms (it was previously also called eo2). This theory stands at the end …