On homotopy invariance for algebras over colored PROPs
Speaker: Mark Johnson, Penn State
Abstract: Colored PROPs are a generalization of (colored) operads, built to allow two types of compositions, called horizontal and vertical. One motivation for this extension away from operads involves the so-called chain Segal PROP, whose algebras can be taken as a definition of Topological Conformal Field Theories. For some purposes, it is unfortunate that these algebra structures are not in any sense homotopy invariant. However, by taking a sort of CW approximation, one can produce a new PROP whose algebras are essentially homotopy invariant, as well as having their own well-behaved homotopy theory. The talk will mainly focus on describing the various structures involved and on properties (including existence) of the associated homotopy theories.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm