##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Lauren Wickman

#### University of Florida

## Knaster Continua and Projective Fraïssé Theory

##### Abstract:

The Knaster continuum, also known as the buckethandle, or the Brouwer–Janiszewski–Knaster continuum can be viewed as an inverse limit of 2-tent maps on the interval. However, there is a whole class (with continuum many non-homeomorphic members) of Knaster continua, each viewed as an inverse limit of p-tent maps, where p is a sequence of primes. In this talk, for each Knaster continuum K, we will give a projective Fraïssé class of finite objects that approximate K (up to homeomorphism) and examine the combinatorial properties of that the class (namely whether the class is Ramsey or if it has a Ramsey extension). We will give an extremely amenable subgroup of the homeomorphism group of the universal Knaster continuum.

Host: Brandon Seward

### February 10, 2022

### 12:00 PM

Zoom ID: 967 4109 3409

Email an organizer for the password

Research Areas

Ergodic Theory and Dynamical Systems****************************