/pdf/an-enumeration-of-surfaces-in-four-space-1xixco0919.pdf

An enumeration of surfaces in four-space

* Introduction* Knots and links in $S^3$* Grid diagrams* Grid homology* The invariance of grid homology* The unknotting number and $\tau$* Basic properties of grid homology* The slice genus and $\tau$* The oriented skein exact sequence* Grid homologies of alternating knots* Grid homology for links* Invariants of Legendrian and transverse knots* The filtered grid complex* More on the filtered chain complex* Grid homology over the integers* The holomorphic theory* Open problems* Homological algebra* Basic theorems in knot theory* Bibliography* Index

Grid Homology for Knots and Links

The triple point number of an embedded surface in 4-space is the minimal number of the triple points on all the projection images into 3-space. We show that the 2-twist-spun trefoil has the triple point number four.

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Suzuki Shin'ichi

Papers

Descriptions on Surfaces in Four-Space I Normal Forms