I've noticed a couple of conference titles which reference something called "topology in dimension 3.5," such as this one and this one. This subject seems quite mysterious to me — it looks like it's part of geometric topology, but I'm guessing it's not about 3.5-dimensional manifolds, so what kinds of things are studied in 3.5-dimensional topology?
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asked Mar 23, 2018 at 21:07
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5$\begingroup$ The conference memoralizing Tim Cochran you reference was so named because Tim’s research focused on knot concordance, which studies how 3-dimensional objects (knots) interact with 4-manifolds. $\endgroup$– Andy PutmanCommented Mar 23, 2018 at 21:13
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4$\begingroup$ Looking at abstracts, it sounds like just a joke, to mean relations between 3-dim and 4-dim topology. $\endgroup$– YCorCommented Mar 23, 2018 at 21:15
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19$\begingroup$ Indeed, the reference to "3.5" is a joke, meant to imply that someone spends half their time on 3 dimensions, and half on 4 dimensions, so on average spends their time thinking about 3.5 dimensions. Moreover, for the conference for Thompson, Scharlemann and Kirby, Thompson is principally known for studying 3 dimensional manifolds, Scharlemann 3 & 4, and Kirby 4 dimensions (although this is not strictly true). Moreover, they are turning 60, 70 and 80 this year, so 20 x the "dimensions". Even though I'm on the organizing committee, I don't claim responsibility for the conference title. $\endgroup$– Ian AgolCommented Mar 23, 2018 at 21:48
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$\begingroup$ @IanAgol AndyPutman YCor thank you all for the answers! I guess something mixing 3- and 4-dimensional topology was probably the most reasonable definition. $\endgroup$– Arun DebrayCommented Mar 26, 2018 at 3:48
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cw answer: As mentioned in the comments, this just refers to the relations between 3-dimensional and 4-dimensional topology.