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

Descriptions on Surfaces in Four-Space I Normal Forms

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

background

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.

/pdf/the-2-twist-spun-trefoil-has-the-triple-point-number-four-26nif49lbm.pdf

Descriptions on Surfaces in Four-Space I Normal Forms

Citations

An enumeration of surfaces in four-space

Grid Homology for Knots and Links

The 2-twist-spun trefoil has the triple point number four

A characterization of groups of closed orientable surfaces in 4-space

Cobordism, homotopy and homology of graphs in R3

Related Papers (5)

An enumeration of surfaces in four-space

On a calculus for 2-knots and surfaces in 4-space

The homotopy groups of knots i. how to compute the algebraic 2-type

A Survey of Knot Theory

Proposals for unknotted surfaces in four-spaces