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Lectures on Heegaard Floer Homology
, 2005
"... These are notes for the second lecture course on Heegaard Floer homology in ..."
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These are notes for the second lecture course on Heegaard Floer homology in
On the Heegaard Floer Homology of . . .
, 2004
"... Assume that the oriented 3manifold M = S 3 −p/q(K) is obtained by a rational surgery (with coefficient −p/q < 0) along an algebraic knot K ⊂ S 3. We compute the Heegaard Floer homology of −M in terms of p/q and the Alexander polynomial of K. ..."
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Assume that the oriented 3manifold M = S 3 −p/q(K) is obtained by a rational surgery (with coefficient −p/q < 0) along an algebraic knot K ⊂ S 3. We compute the Heegaard Floer homology of −M in terms of p/q and the Alexander polynomial of K.
On the Heegaard Floer Homology of a . . .
, 2006
"... We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S 1. We determine HF + (Σg × S¹, s; C) completely in the case c1(s) = 0, which for g ≥ 3 was previously unknown. We show that in this case HF ∞ is closely related to the cohomology of a th ..."
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We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S 1. We determine HF + (Σg × S¹, s; C) completely in the case c1(s) = 0, which for g ≥ 3 was previously unknown. We show that in this case HF ∞ is closely related to the cohomology of a
The Heegaard Floer Homology of a . . .
, 2005
"... We calculate the Heegaard Floer homology groups ̂ HF(Y, s0), HF + (Y, s0) and HF ∞ (Y, s0) for Y the product of a genus g surface with a circle and s0 the torsion spin c structure. This has previously been calculated by Peter Ozsváth and Zoltán Szabó only for the cases of g = 0, 1, 2 (see [3, 5, 8] ..."
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We calculate the Heegaard Floer homology groups ̂ HF(Y, s0), HF + (Y, s0) and HF ∞ (Y, s0) for Y the product of a genus g surface with a circle and s0 the torsion spin c structure. This has previously been calculated by Peter Ozsváth and Zoltán Szabó only for the cases of g = 0, 1, 2 (see [3, 5, 8
Topics in Heegaard Floer homology
, 2009
"... Heegaard Floer homology is an extremely powerful invariant for closed oriented threemanifolds, introduced by Peter Ozsváth and Zoltán Szabó. This invariant was later generalized by them and independently by Jacob Rasmussen to an invariant for knots inside threemanifolds called knot Floer homology ..."
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Heegaard Floer homology is an extremely powerful invariant for closed oriented threemanifolds, introduced by Peter Ozsváth and Zoltán Szabó. This invariant was later generalized by them and independently by Jacob Rasmussen to an invariant for knots inside threemanifolds called knot Floer
HEEGAARD–FLOER HOMOLOGY FOR SINGULAR KNOTS
, 2007
"... Using the combinatorial description for knot Heegaard–Floer homology, we give a generalization to singular knots which does fit in the general program of categorification of Vassiliev finite–type invariants theory. ..."
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Using the combinatorial description for knot Heegaard–Floer homology, we give a generalization to singular knots which does fit in the general program of categorification of Vassiliev finite–type invariants theory.
HEEGAARDFLOER HOMOLOGY AND STRING LINKS
, 2006
"... In [14] P. Ozsváthand Z. Szabóuse the technology of HeegaardFloer homology to refine the AlexanderConway polynomial of a marked knot in S3. In particular, they define KnotFloer homology groups for relative Spinc structures that correspond to the terms in the polynomial: the Euler characteristic o ..."
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In [14] P. Ozsváthand Z. Szabóuse the technology of HeegaardFloer homology to refine the AlexanderConway polynomial of a marked knot in S3. In particular, they define KnotFloer homology groups for relative Spinc structures that correspond to the terms in the polynomial: the Euler characteristic
Heegaard Floer homology and alternating knots
, 2002
"... In [23] we introduced a knot invariant for a nullhomologous knot K in an oriented threemanifold Y, which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the threesphere. We give a combinato ..."
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Cited by 85 (17 self)
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In [23] we introduced a knot invariant for a nullhomologous knot K in an oriented threemanifold Y, which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the threesphere. We give a
On the contact class in Heegaard Floer homology
"... ABSTRACT. We present an alternate description of the OzsváthSzabó contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M, ξ) has an adapted open book decomposition whose page S is a oncepunctured torus, then the monodromy is rightveering if and o ..."
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Cited by 36 (5 self)
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ABSTRACT. We present an alternate description of the OzsváthSzabó contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M, ξ) has an adapted open book decomposition whose page S is a oncepunctured torus, then the monodromy is rightveering
Results 1  10
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646