Topology Proceedings 30 No. 1 (2006), pp. 223-236

Ends of 4-Manifolds

Sandy Ganzell

We define and study a measurement of complexity for the ends of 4-manifolds. Bounds on this complexity are computed for an important family of exotic R⁴'s, and we show how a particular exotic R⁴ of high complexity can be used to corrupt the ends of 4-manifolds, resulting in a proof that many open 4-manifolds have infinitely many smooth structures.

Keywords: embedded 3-manifolds, exotic R⁴, 4-manifolds, smooth structures

Mathematics Subject Classification: Primary 57N13 57R55

Document formats: PDF file 245.4 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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