シャドウ複雑度による4次元多様体のコルクおよびエキゾチック微分構造の研究

Tohoku University石川昌治課

The special shadow-complexity of #k(S1×S3)\#_k(S^1\times S^3)

The special shadow-complexity is an invariant of closed $4$-manifolds defined by Costantino using Turaev's shadows. We show that for any positive integer $k$, the special shadow-complexity of the connected sum of $k$ copies of $S^1\times S^3$ is exactly $k+1$.Comment: 12 pages, 6 figure

Positive flow-spines and contact 3-manifolds

We say that a contact structure on a closed, connected, oriented, smooth 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. We then define a map from the set of positive flow-spines to the set of contact 3-manifolds up to contactomorphism by sending a positive flow-spine to the supported contact 3-manifold and show that this map is well-defined and surjective. We also determine the contact 3-manifolds supported by positive flow-spines with up to 3 vertices. As an application, we introduce the complexity for contact 3-manifolds and determine the contact 3-manifolds with complexity up to 3.Comment: 73 pages, 78 figures. The last subsection was remove