Title: | Multicomplexes and their applications |

Seminar: | Topology/Geometry Seminar |

Speaker: | David Hurtubise, Penn State |

Abstract: |

A multicomplex is a bigraded R-module X_pq with homomorphisms d_i:X_pq ---> X_p-i,q+i-1 such that \sum_{i+j = n} d_i d_j = 0 for all n. A multicomplex can often be assembled to form a chain complex (C,d) where the differential is given by the sum d = d_0 + d_1 +.... A bicomplex is an example of a multicomplex where d_i = 0 for all i > 1.
Multicomplexes appear in several contexts in the literature and have sometimes been confused with spectral sequences. In this talk I will give a survey of multicomplexes and their applications. |