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Spherical Seifert fibered spaces, kn...

Doig, Margaret I.

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Spherical Seifert fibered spaces, knot surgeries, and Heegaard Floer homology.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spherical Seifert fibered spaces, knot surgeries, and Heegaard Floer homology./
作者:	Doig, Margaret I.
面頁冊數:	94 p.
附註:	Source: Dissertation Abstracts International, Volume: 71-10, Section: B, page: 6154.
Contained By:	Dissertation Abstracts International71-10B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3424104
ISBN:	9781124230818

Spherical Seifert fibered spaces, knot surgeries, and Heegaard Floer homology.
Doig, Margaret I.

Spherical Seifert fibered spaces, knot surgeries, and Heegaard Floer homology. - 94 p.

Source: Dissertation Abstracts International, Volume: 71-10, Section: B, page: 6154.

Thesis (Ph.D.)--Princeton University, 2010.

Thanks to Wallace and Lickorish, we know that any 3-manifold can be obtained by surgery on a link. In 1971, Moser asked which of these manifolds can be obtained from surgery on a knot. On the other hand, Berge and then Dean et al. tried to determine which knots give rise to given types of 3-manifold, in particular lens spaces and Seifert fibered spaces. We use Heegaard Floer theory to investigate these two questions using a set of invariants for a 3-manifold and its associated torsion Spinc structures called the correction terms. These terms can be calculated combinatorially either from a plumbing description of the manifold or from a knot surgery description. We show that the correction terms provide an obstruction to spherical Seifert fibered spaces (other than lens spaces) being realized as knot surgeries. For those spaces with small first homology, we show the invariant is a complete obstruction; we give reasons why it should also be useful for those with larger homology.

ISBN: 9781124230818Subjects--Topical Terms:

515831
Mathematics.

Spherical Seifert fibered spaces, knot surgeries, and Heegaard Floer homology.
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500 $a Source: Dissertation Abstracts International, Volume: 71-10, Section: B, page: 6154.
500 $a Adviser: Zoltan Szabo.
502 $a Thesis (Ph.D.)--Princeton University, 2010.
520 $a Thanks to Wallace and Lickorish, we know that any 3-manifold can be obtained by surgery on a link. In 1971, Moser asked which of these manifolds can be obtained from surgery on a knot. On the other hand, Berge and then Dean et al. tried to determine which knots give rise to given types of 3-manifold, in particular lens spaces and Seifert fibered spaces. We use Heegaard Floer theory to investigate these two questions using a set of invariants for a 3-manifold and its associated torsion Spinc structures called the correction terms. These terms can be calculated combinatorially either from a plumbing description of the manifold or from a knot surgery description. We show that the correction terms provide an obstruction to spherical Seifert fibered spaces (other than lens spaces) being realized as knot surgeries. For those spaces with small first homology, we show the invariant is a complete obstruction; we give reasons why it should also be useful for those with larger homology.
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
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792 $a 2010
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