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# Topology - Continuum Theory

DMS Topology Seminar
Jan 31, 2018 02:00 PM
Parker Hall 246

Speaker: Stu Baldwin

Title: Inverse Limits of Flexagons

Abstract: Flexagons were first introduced in 1939 by Arthur H. Stone when he was a graduate student at Princeton, and they were popularized by Martin Gardner in the December 1956 issue of Scientific American in an article entitled "Flexagons" which launched his well known "Mathematical Games" column, which appeared in that magazine for many years.  By folding strips of paper into various geometrical shapes, Stone created a variety of different flexagons, of which the most elegant are the "hexaflexagons" created by folding strips of equilateral triangles into a hexagonal shape and attaching the ends.

Mathematical studies of flexagons have concentrated on the combinatorial properties of flexagons created with a finite number of polygons.  Here, we consider an infinite version which can be created either using inverse limits or nested intersections of solid tori (viewed as a folded annulus cross the unit interval). If $n \ge 3$, then a strip of $3n$ equilateral triangles can be folded into a hexaflexagon which (after the ends are identified) is topologically an annulus if $n$ is even and a Möbius strip if $n$ is odd.  Of these, the most natural ones are created using $9(2^n)$ triangles, leading to the construction of a space (via either inverse limits or nested intersections) which (viewed as a subset of $\mathbb{R}^3$ in a natural way) mimics the properties of all of the hexaflexagons having finitely many triangles.  Some preliminary results on the properties of this space will be discussed.

(Paper toys will be provided to the audience as visual aids.)

Continuum Theory Seminar
Feb 22, 2016 04:00 PM
Parker Hall 224

Piotr Minc will continue today talking about compactifications of the ray.
Continuum Theory Seminar
Feb 15, 2016 04:00 PM
Parker Hall 224

Piotr Minc will talk today about the work he’s done on certain compactifications for METRIC spaces.
Continuum Theory Seminar
Feb 08, 2016 04:00 PM
Parker Hall 224

Michel Smith will continue (and possibly conclude) his presentation on the non-metric pseudo-arc
Continuum Theory Seminar
Feb 01, 2016 04:00 PM
Parker Hall 224

Speaker: Michel Smith

Topic: some properties of the non-metric pseudo-arc relevant to the Wood’s Conjecture

Continuum Theory Seminar
Jan 25, 2016 04:00 PM
Parker Hall 224

Speakers: Michel Smith

Topic: joint work with Jan Boronski--pseudo-circle and non-metric pseudo-arc and counter examples to the Wood's conjecture

Joint Continuum Theory and Set Theoretic Topology Seminar
Sep 28, 2015 04:00 PM
Parker Hall 247 +/-1

Speaker: David Lipham

Title: 2^c  different subcontinua of (C(H*) (where H* = βH - H)  none of which are in H* (and where C(X) is the hyperspace of subcontinua of  X.)

Continuum Theory
Sep 21, 2015 03:00 PM
Parker Hall 246

Dr. Baldwin will speak on "Homeomorphism Classes of Solenoids"
Continuum Theory Seminar
Sep 14, 2015 04:00 PM
Parker Hall 246(?)

Speaker: Steven Clontz ('15), University of North Carolina at Charlotte

Steven will talk about a couple of topological games he has been considering.

Abstract: A Corson compact space is a compact space which may be embedded in a Sigma-product of real lines; a Sigma-product of real lines is the collection of sequences in $$\mathbb R^\kappa$$ for some cardinal $$\kappa$$ for which all but countably many coordinates are zero. In particular, compact metrizable spaces are Corson compact. Clontz will speak about a joint result with Scott Varagona (University of Montevallo) showing that any generalized inverse limit of length $$\kappa$$ obtained with a non-trivial idempotent continuum-valued u.s.c. bonding map is not Corson compact.