On exotic embeddings of submanifolds in 4-manifolds - Anubhav Mukherjee

Mathematics Department Colloquium - December 7, 2023
Stony Brook University

Anubhav Mukherjee, Princeton University

Abstract: Understanding the existence of those phenomena that hold true in the topological category but not in the smooth category (known as exotic phenomena) are the central topics of study in 4-dimensional topology. An important principle in 4-dimensional topology, as discovered by Wall in the 1960s, states that all exotic phenomena on compact 4-manifolds are eliminated by sufficiently many stabilizations (i.e., taking connected sum with S^2—S^2). Since then, it has been a fundamental problem to search for exotic phenomena that survive some number of stabilizations. In this talk I will discuss how one can construct exotic embeddings of submanifolds (surfaces and 3-manifolds) in 4-manifolds that can survive such stabilizations.