**AAS Meeting #194 - Chicago, Illinois, May/June 1999**

*Session 70. Astronomy and Education*

Display, Wednesday, June 2, 1999, 10:00am-6:30pm, Southwest Exhibit Hall
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## [70.07] Visualizing the Big Bang: An Introduction to Topology and 3-Manifolds for Undergraduates

*R.B. Gardner (East Tennessee State University)*

A popular tool used in freshman astronomy classes is the
``balloon analogy'' of the universe. In this analogy, we
imagine ourselves as two-dimensional inhabitants of the
surface of a swelling sphere. This model of the universe has
the desirable properties that it (1) has no edge, (2) has no
center, and (3) satisfies Hubble's Law. Also, this model has
spherical geometry and a finite amount of ``space.'' When
discussing the other possible geometries of the universe
(namely, Euclidean and hyperbolic), the two-dimensional
analogies used are usually the Euclidean plane and the
hyperbolic parabaloid (respectively). These surfaces have
the desired curvatures and geometries. However, many
students get the impression from these examples that a space
with zero or negative curvature *must* be infinite. This
is not the case.

In this presentation, an informal description of 3-manifolds
and their topology will be given. A catalogue of
topologically distinct manifolds will be presented,
including those which have zero and negative curvature, yet
have finite volume. Models of the universe in terms of these
manifolds will be introduced. Finally, empirical methods for
determining which 3-manifold represents the topology of our
universe will be described.

If the author provided an email address or URL for general inquiries, it is a
s follows:

http://www.etsu.edu/math/gardner/gardner.htm

gardnerr@etsu.edu

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