Title: | Gerbes, principal 2-group bundles and characteristic classes |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Mathieu Stienon, Penn State |

Abstract: |

Note: This is a special lecture and will be in Room 114 McAllister.
It is well known that a principal $G$-bundle $P$ over a manifold $M$ determines a homotopy class of maps $f$ from $M$ to the classifying space $BG$ of the group $G$. Pulling back the generators of $H^*(BG)$ through $f$, one obtains characteristic classes of the principal bundle $P$ over $M$. It is a classical theorem of Chern and many others that these characteristic classes coincide with those obtained from the Chern-Weil construction using connections and curvatures.
Gerbes are higher order analogues of principal bundles. We will discuss an
analogue of Chern's theorem for gerbes. The idea is to relate Gerbes to 2-group principal bundles, and to study characteristic classes of these principal 2-group bundles. Recently, physicists motivated by string theory have been increasingly interested in 2-group bundles. |