connected sum

The connected sum of knots $K$ and $J$ is a knot, denoted by $K\\#J$ ,constructed by removing a short segment from each of $K$ and $J$ and joining each free end of $K$ to a different free end of $J$ to form a new knot. The connected sum of two knots always exists but is not necessarily unique.

The connected sum of oriented knots $K$ and $J$ is a connected sum of knots which has a consistent orientation inherited from that of $K$ and $J$ . This sum always exists and is unique.

Example.

Suppose $K$ and $J$ are both the trefoil knot.

By one choice of segment deletion and reattachment, $K\\#J$ is the quatrefoil knot.

单词	ConnectedSum
释义	connected sum The connected sum of knots $K$ and $J$ is a knot, denoted by $K\\#J$ ,constructed by removing a short segment from each of $K$ and $J$ and joining each free end of $K$ to a different free end of $J$ to form a new knot. The connected sum of two knots always exists but is not necessarily unique. The connected sum of oriented knots $K$ and $J$ is a connected sum of knots which has a consistent orientation inherited from that of $K$ and $J$ . This sum always exists and is unique. Example. Suppose $K$ and $J$ are both the trefoil knot. Figure 1: The trefoil knot By one choice of segment deletion and reattachment, $K\\#J$ is the quatrefoil knot. Figure 2: $K\\#J$ is the quatrefoil knot
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