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On the twisted Floer homology of map...

Fink, Evan.

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On the twisted Floer homology of mapping tori of periodic diffeomorphisms.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the twisted Floer homology of mapping tori of periodic diffeomorphisms./
Author:	Fink, Evan.
Description:	122 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-09, Section: B, page: 5506.
Contained By:	Dissertation Abstracts International71-09B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3420703
ISBN:	9781124174167

On the twisted Floer homology of mapping tori of periodic diffeomorphisms.
Fink, Evan.

On the twisted Floer homology of mapping tori of periodic diffeomorphisms. - 122 p.

Source: Dissertation Abstracts International, Volume: 71-09, Section: B, page: 5506.

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

Let K ⊂ Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered manifold, in terms of twisted knot Floer homology. Using this, we compute the twisted Heegaard Floer homology HF + of the mapping torus of a diffeomorphism of a closed Riemann surface whose mapping class is periodic, giving an almost complete description of the structure of these groups. When the surface is of genus at least three and the mapping class is nontrivial, we find in particular that in the "second-to-highest level" of Spinc structures, this is isomorphic to a free module (over a certain ring) whose rank is equal to the Lefschetz number of the diffeomorphism. After taking a tensor product with Z/2Z , this agrees precisely with the symplectic Floer homology of the diffeomorphism, as calculated by Gautschi.

ISBN: 9781124174167Subjects--Topical Terms:

1669109
Applied Mathematics.

On the twisted Floer homology of mapping tori of periodic diffeomorphisms.
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020 $a 9781124174167
035 $a (UMI)AAI3420703
035 $a AAI3420703
040 $a UMI $c UMI
100 1 $a Fink, Evan. $3 1672764
245 1 0 $a On the twisted Floer homology of mapping tori of periodic diffeomorphisms.
300 $a 122 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-09, Section: B, page: 5506.
500 $a Adviser: Peter Ozsvath.
502 $a Thesis (Ph.D.)--Columbia University, 2010.
520 $a Let K ⊂ Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered manifold, in terms of twisted knot Floer homology. Using this, we compute the twisted Heegaard Floer homology HF + of the mapping torus of a diffeomorphism of a closed Riemann surface whose mapping class is periodic, giving an almost complete description of the structure of these groups. When the surface is of genus at least three and the mapping class is nontrivial, we find in particular that in the "second-to-highest level" of Spinc structures, this is isomorphic to a free module (over a certain ring) whose rank is equal to the Lefschetz number of the diffeomorphism. After taking a tensor product with Z/2Z , this agrees precisely with the symplectic Floer homology of the diffeomorphism, as calculated by Gautschi.
590 $a School code: 0054.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a Columbia University. $3 571054
773 0 $t Dissertation Abstracts International $g 71-09B.
790 1 0 $a Ozsvath, Peter, $e advisor
790 $a 0054
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3420703