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Dehn filling: A survey

C. Gordon (1998)

Banach Center Publications

In this paper we give a brief survey of the present state of knowledge on exceptional Dehn fillings on 3-manifolds with torus boundary. For our discussion, it is necessary to first give a quick overview of what is presently known, and what is conjectured, about the structure of 3-manifolds. This is done in Section 2. In Section 3 we summarize the known bounds on the distances between various kinds of exceptional Dehn fillings, and compare these with the distances that arise in known examples. In...

Dehn twists on nonorientable surfaces

Michał Stukow (2006)

Fundamenta Mathematicae

Let t a be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, I ( t a ( b ) , b ) = | n | I ( a , b ) ² , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...

Deloopings of the spaces of long embeddings

Keiichi Sakai (2014)

Fundamenta Mathematicae

The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two). In this paper we deloop the homotopy fiber to obtain the topological Stiefel manifold, combining results of Lashof and of Lees. We also give a delooping of the long embedding space, which can be regarded as a version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of the disk relative to the boundary....

Delta link-homotopy on spatial graphs.

Ryo Nikkuni (2002)

Revista Matemática Complutense

We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the...

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