Bing’s House

Cool diagrams

Sketches of Topology

So there’s this example of a 2-complex that’s contractible, but not obviously so. Well actually, once you see it, it’s not too hard to see. Bing’s house with two rooms.

Picture 12

Blah. It’s not so apparent what’s going on. It’s a 2-complex, so let’s draw in the relevant 1-complex.

Picture 13

You can see two vertices and four edges. The surfaces of this 2-complex are all disks, and they make threefold incidences to the edges. The two loop edges bound disks, but they don’t show up since they’re the same translucent color as everything else. And all the corners can be somewhat misleading… Here’s a slicker picture with those two disks colored.

BingsHouse-smooth

There has recently been a few words about it at MathOverflow where it’s pointed out that the contractiblity of Bing’s house is explained in Hatcher’s text and Cohen’s text. In this post, let’s see how this contraction works.

View original post 248 more words

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About varasdemate

n00bie blogger, just recently getting the hang of blogging
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