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# Oguz Savk : Bridging the gaps between homology planes and Mazur manifolds.

We call a non-trivial homology 3-sphere a Kirby-Ramanujam sphere if it bounds a homology plane, an algebraic complex smooth surface with the same homology groups of the complex plane. In this talk, we present several infinite families of Kirby-Ramanujam spheres bounding Mazur type 4-manifolds, compact contractible smooth 4-manifolds built with only 0-, 1-, and 2-handles. Such an interplay between complex surfaces and 4-manifolds was first observed by Ramanujam and Kirby around nineteen-eighties. This is upcoming joint work with Rodolfo Aguilar Aguilar.

**Category**: Geometry and Topology,Uploaded Videos**Duration**: 47:41**Date**: October 24, 2022 at 3:15 PM-
**Tags:**seminar, geometry and topology

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