# Geometric topology

There have been 1 completed talk and 5 topic suggestions tagged with **geometric topology**.

## Related Tags

- topology
- algebraic topology
- knot theory
- geometry
- multivariate calculus
- module theory
- homology
- differential geometry

## Completed Talks

### Quandles: The Algebra of Knots

Delivered by Brennen Creighton-Young on Friday November 25, 2016

One of the major goals of knot theory is to determine whether or knot two knots can be continuously deformed into one another. This idea can be fully captured algebraically — and leads us to algebraic structures that not only capture the desired notion of knot deformations, but reveal themselves as truly fascinating mathematical objects. We will use only linear algebra and elementary abstract algebra.

Though continuous deformation is a straight forward idea, the rigorous definition of this, the notion of ambient isotopy, is practically unusable. This talk will provide a quick overview of basic knot theory and will work towards developing numerous algebraic strategies to identify when two knots are ambient isotopic. We will focus mostly on providing motivation for keis, an algebraic representation of knots, as well as their generalization, quandles. Quandles will prove to be not only helpful with respect to the goal of the classification of knots, but also as rich algebraic structures. The talk will involve small amounts of group theory, linear algebra and module theory.

## Talk Suggestions

### Low Dimensional Geometry

Possible reference materials for this topic include

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geometric topology geometry multivariate calculus topology

### Penrose Tilings

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geometric topology geometry topology

### Rational Tangles and Conway's Theorem

Possible reference materials for this topic include

C. C. Adams : The Knot Book: An elementary introduction to the mathematical theory of knots

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geometric topology knot theory topology

### The Jordan Curve Theorem

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algebra algebraic topology geometric topology homology topology

### The Winding Number

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algebra algebraic topology analysis differential geometry geometric topology geometry topology