726 research outputs found
Elliptic Involution in Bordered Heegaard Floer Homology
No full textIn this thesis, we study the elliptic involution from the point of view of the bordered Heegaard Floer homology.
We show that the bordered Heegaard Floer invariant CFD^hat of a knot complement in S^3 is invariant under the elliptic involution on its boundary. As a computational result, we demonstrate how the bordered Heegaard Floer invariant CFDA^hat associated to the elliptic involution affects such CFD^hat complexes via A infinity tensor product. Globally, it "flips" the entire complex, while locally, it modifies the complex nicely in an arrow-wise fashion. The latter local description can be extended to quarter boundary Dehn twists as well.
Additionally, the Heegaard Floer homology of the associated open book decomposition to the elliptic involution is computed
Clay Mathematics Proceedings An introduction to Heegaard Floer homology
No full text2. Heegaard decompositions and diagrams 2 3. Morse functions and Heegaard diagrams 7 4. Symmetric products and totally real tori
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Combinatorial Heegaard Floer homology and nice Heegaard diagrams
No full textAbstract We consider a stabilized version of cHF of a 3–manifold Y (i.e.
the U = 0 variant of Heegaard Floer homology for closed 3–manifolds).
We give a combinatorial algorithm for constructing this invariant, starting
from a Heegaard decomposition for Y , and give a topological proof of its
invariance properties
Heegaard splittings and the tight Giroux Correspondence
No full textThis paper presents a new proof of the Giroux Correspondence for tight contact 3-manifolds using techniques from Heegaard splittings and convex surface theory. We introduce tight Heegaard splittings of arbitrary contact 3–manifolds; these generalise the Heegaard splittings naturally induced by an open book decomposition adapted to a contact structure on the underlying manifold. Via a process called refinement, any tight Heegaard splitting determines an open book, up to positive open book stabilisation. This allows us to translate moves relating distinct tight Heegaard splittings into moves relating their associated open books. We use this relationship to show that every Heegaard splitting of a contact 3-manifold may be stabilised to a Heegaard splitting induced by a supporting open book decomposition. Finally, wLzlky+/YAPZGnp+ZUWbUEfN2BNYqwe prove the tight Giroux Correspondence, showing that any pair of open book decompositions supporting a fixed tight contact structure become isotopic after a sequence of positive open book stabilisations and destabilisations.This material is based in part upon work supported by the National Science Foundation under Grant No. DMS-1929284 while the authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Braids program. The first author received support from the Australian National University\u2019s Outside Studies Program and the second author was supported by the FWF grant \u201CCut and Paste Methods in Low Dimensional Topology\u201D P 34318. The second author would like to thank the the Erd\u00F6s Center for providing a friendly and calm environment. Both authors appreciate the helpful feedback provided by the referee.Peer-reviewe
Applications of Heegaard Floer Homology to Knot Concordance
No full textWe consider several applications of Heegaard Floer homology to the study of knot concordance.
Using the techniques of bordered Heegaard Floer homology, we compute the concordance invariant for a family of satellite knots that generalizes Whitehead doubles.
We also construct an integer lift of the concordance invariant . We introduce an interpretation of in terms of a filtration on \cfhat(S^3_N K) induced by a family of knots .
Finally, we use truncated Heegaard Floer homology to construct a sequence of concordance invariants that generalizes previously known concordance invariants , , and
The surgery exact triangle in Heegaard Floer homology
No full textWe define Heegaard Floer homology for closed oriented three-manifolds and present the
proof and immediate applications of the surgery exact triangle
Satellite knots and immersed Heegaard Floer homology
No full textWe describe a new method for computing the UV=0 knot Floer complex of a satellite knot given the UV=0 knot Floer complex for the companion and a doubly pointed bordered Heegaard diagram for the pattern, showing that the complex for the satellite can be computed from an immersed doubly pointed Heegaard diagram obtained from the Heegaard diagram for the pattern by overlaying the immersed curve representing the complex for the companion. This method streamlines the usual bordered Floer method of tensoring with a bimodule associated to the pattern by giving an immersed curve interpretation of that pairing, and computing the module from the immersed diagram is often easier than computing the relevant bordered bimodule. In particular, for (1,1) patterns the resulting immersed diagram is genus one, and thus the computation is combinatorial. For (1,1) patterns this generalizes previous work of the first author which showed that such immersed Heegaard diagram computes the V=0 knot Floer complex of the satellite. As a key technical step, which is of independent interest, we extend the construction of a bigraded complex from a doubly pointed Heegaard diagram and of an extended type D structure from a torus-boundary bordered Heegaard diagram to allow Heegaard diagrams containing an immersed alpha curve
Two questions on Heegaard diagrams of S3.
No full textAn important open question about 3-manifolds is whether or not there exists an algorithm for recognizing S3. The author poses two questions about Heegaard diagrams of S3, appropriate answers to either of which would give such an algorithm.
If a Heegaard diagram contains either a wave or a cancelling pair, then one can find an equivalent diagram of smaller complexity (in the latter case, of smaller genus). Every nontrivial genus-2 diagram of S3 contains a wave [T. Homma, M. Ochiai and M. Takahashi Osaka J. Math 17 (1980), no. 3, 625–648; MR0591141 (82i:57013)], but this is false for higher genera. The author's first question is whether there are any Heegaard diagrams of S3 without waves and without cancelling pairs. {Reviewer's remark: An example of such a diagram is contained in an article of Ochiai [ibid. 22 (1985), no. 4, 871–873; MR0815455 (87a:57020)].}
Given a Heegaard diagram, there is a reduction procedure which produces a so-called pseudominimal diagram. W. Haken [in Topology of manifolds (Athens, Ga., 1969), 140–152, Markham, Chicago, Ill., 1970; MR0273624 (42 #8501)] has suggested that perhaps the only pseudominimal diagrams of S3 are the trivial ones; no counterexamples are known. The author suggests a further reduction step which might be applied to a pseudominimal diagram, yielding several partial diagrams. If any of these has a cancelling pair, then the genus of the original diagram can be reduced. An example is given to show that, in general, for manifolds different from S3, even this enhanced procedure does not always detect the reducibility of a Heegaard splitting. The author's second question, however, is whether it does for splittings of S3. Thus the author is suggesting a possible algorithm for recognizing S3 which allows for the existence of nontrivial pseudominimal diagrams of S3.Comité Conjunto Hispano-NorteamericanoNSFDepto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu
Substrate-specific detection on nitrocellulose of SDS-PAGE separated enzymes employing polyspecific antibodies and secondary incubation with native enzyme mixture
No full textOptimal combinations of acute phase proteins for detecting infectious disease in pigs
No full textPeer reviewe
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