分野別セミナー

Let $X$ be a path-connected pointed topological space and $G$ be a topological group. Given a principal $G$-bundle $P\to X$, the group of bundle automorphisms covering the identity on $X$ is called the gauge group. Endowed with the compact-open topology, the gauge group of $P\toX$ is homotopy equivalent to the loop space of the path component of the mapping space $Map(X,BG)$ containing the map that classifies the bundle. The topology of the gauge groups and their classifying spaces has played an important role in other areas of mathematics such as mathematical physics and differential geometry. Although the set of isomorphism classes of principal $G$-bundles over a finite $CW$-complex $X$ might be infinite, there exist only finitely many distinct homotopy types among the gauge groups. One approach to the homotopy classification problem of gauge groups is to obtain decompositions of the gauge groups. In this talk I will present some results on homotopy decompositions of gauge groups over connected sums of sphere bundles over spheres when $G$ is a simply connected simple compact Lie group.


8月23日(木)に
Universidade da CoruñaのCristina Costoyaさんと
University of SouthamptonのIngrid Membrillo Solisさん
をお招きして、トポロジーセミナーを開催します。
皆様奮ってご参加ください。
！！ いつもと曜日と時刻が異なるのでご注意ください ！！