On exotic embeddings of submanifolds in 4-manifolds - Anubhav Mukherjee
Автор: Stony Brook Mathematics
Загружено: 2023-12-12
Просмотров: 1237
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.
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