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# Reading Topology from Open Books (Prof. Bahar Acu, Pitzer College)

## March 29, 2023 @ 4:15 pm - 5:30 pm

**Title: **Reading Topology from *Open Books*

**Speaker:** Bahar Acu, Department of Mathematics, Pitzer College

**Abstract: **How can we study topological shapes that are outside the realm of our imagination? In this talk, we will explore potential answers to that question by diving deep into dimensionality and topology via open books. Topology is the study of properties of shapes that do not fundamentally change when they are bent and/or stretched without poking holes or ripping apart. At this point, you must have heard that to a topologist, a donut and a coffee cup (with a handle) are the same thing since one can be deformed into the other continuously, i.e. only via bending and/or stretching. A very useful strategy in studying topological objects (in our case, *manifolds*) is to factor them into smaller pieces. An *open book decomposition *of an n-dimensional manifold (the open book) is a special function that helps us study our object in terms of its (n-1)-dimensional fibers (the pages) and (n-2)-dimensional boundary of these fibers (the binding). This topological tool provides a natural framework for studying topological properties of certain geometric structures on smooth manifolds such as *contact structures*. For example, every (contact) 3-dimensional manifold can be presented as an open book whose pages are surfaces and binding is a knot/link. In this talk, we will talk about these objects in greater detail with examples.

*Research Directions in Symplectic and Contact Geometry and Topology*, lead-edited by Dr. Acu, was recently published as a part of Springer’s Association for Women in Mathematics Series.