Homotopy classification of 4-manifolds

John Nicholson (University of Glasgow)

Monday 27th November, 2023 16:00-17:00 Maths 311B


In order to classify smooth 4-manifolds up to homeomorphism, and ultimately diffeomorphism, it is first necessary to classify up to homotopy equivalence. Whilst the homotopy classification in the simply connected case is known (modulo a few unknowns), much less is known for non-simply connected 4-manifolds where a number of basic questions remain unanswered. The aim of this talk will be to give a broad overview of the subject and to discuss the various obstacles that would need to be overcome in order to obtain an effective classification. An important idea will be to make use of a close relationship which exists between the homotopy classification of smooth 4-manifolds and that of 2-dimensional CW-complexes.

Add to your calendar

Download event information as iCalendar file (only this event)