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Showing 1 to 20 of 20 for “"Euler characteristic"”.
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Direct Computation of the Degree 4 Gopakumar -Vafa Invariant on a Calabi -Yau 3 -Fold
In this work we compute the topological Euler characteristic of the 17-dimensional moduli space of stable sheaves of Hilbert polynomial 4n + 1 on P2 to be 192, using tools of algebraic geometry. This Euler characteristic is equal up to sign to the degree 4 BPS (Gopakumar-Vafa) invariant of local P …
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Bordered Heegaard Floer Homology, Satellites, and Decategorification
… the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties …
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The Kauffman Bracket and Genus of Alternating Links
… then applying the Seifert algorithm to find the Euler characteristic and genus of its surface. Finally finding the relationship of the Kauffman bracket polynomial and the genus of the alternating links is the main goal of this paper. </p>
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Sequences of compact curvature
… elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will …
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New techniques in calculation of sutured instanton Floer homology: by Heegaard diagrams, Euler characteristics, and Dehn surgery formulae
… technique is based on the identification of Euler characteristics of $SFH$ and $SHI$, from which we obtain a lower bound on the dimension of $SHI$. We construct a decomposition of $SHI$ analogous to the spin$^c$ structure decomposition of $SFH$, and prove that the enhanced Euler …
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Geometric Aspects of Supersymmetric Partition Functions
… interpretation in terms of the equivariant Euler characteristics of the algebraic differential forms on the resolved space. The superconformal symmetries of the quantum mechanics imply certain symmetries of the Euler characteristics. We also explain how holography predicts an asymptotic …
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A new structure on Khovanov's homology
… to the Jones polynomial by taking graded Euler characteristic. Bar-Natan [1] [2] computed this invariant for the prime knots of up to 11 crossings. From the data, Bar-Natan, Garoufalidis, and Khovanov formulated two conjectures on the value of the Khovanov invariant of an alternating knot …
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Problems in number theory and hyperbolic geometry
… real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).
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On total Springer representations
… sum of cohomology groups of a Springer fiber (in characteristic 0), called a total Springer representation, as a representation of both the Weyl group and the stabilizer of the corresponding nilpotent element. For classical types, we present explicit formulas for the decomposition of total …
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Grothendieck Semirings and Definable Endofunctions
… which occur in Model Theory, and also emphasize Euler characteristics, that is, invariant measures simultaneously additive and multiplicative on the classes of objects of such categories. The semiring of any strongly minimal group, as well as the one of any infinite vector space over any division …
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Computations and lower bounds for scl and the relative Gromov seminorm
… Gauß–Bonnet formula leading to estimates of the Euler characteristic. We show in particular that our method yields a new proof of a theorem of Heuer on a sharp spectral gap for right-angled Artin groups.
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Random surface interpretations of two-dimensional Liouville quantum gravity and Yang-Mills theory
… our weight is explicit as ±Nᵡ where χ is the Euler characteristic, for any gauge group U(N), SO(N), Sp(N/2). Based on the well-established continuum theory in two dimensions, we provide a probabilistic treatment for Wilson loop expectations, also leading to various applications like an …
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Line Bundles on Projective Homogeneous Spaces
… spaces G/H for a semisimple algebraic group G in characteristic p $>$ 0, where H is a subgroup scheme containing a Borel subgroup B. In characteristic p $>$ 0 there are an infinite number of subgroup schemes containing B--the reduced ones are the ordinary parabolic subgroups P $\supseteq$ B. …
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Equivariant cohomology, homogeneous spaces and graphs
… the geometry of homogeneous spaces with non-zero Euler characteristic.
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Monopoles and Landau-Ginzburg Models
… theory based on the results from Part I. The Euler characteristic of this Floer homology recovers the Milnor-Turaev torsion invariant of 𝑌 by a classical theorem of Meng-Taubes and Turaev. ∙ In Part III, more topological properties of this Floer theory are explored in the special case that the …
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Generalizations of quasiconvexity for finitely generated groups
… connected, finite type surface with negative Euler characteristic [67]. Finding algorithms for the detection and decidability of various properties of groups is a fundamental theme in geometric group theory. For a word-hyperbolic group G, Kapovich [55] provided a partial algorithm which, on …
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Using 3D Tomography to Understand Fluid-Fluid Interface Evolution in Porous Media for Carbon Sequestration Applications
… including Betti numbers and the corresponding Euler characteristic that are relevant to fluid connectivity for an air-water-sandstone system under ambient conditions. We aimed to investigate the effect of the saturation level of water and image resolution on the REV of the parameters …
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Using 3D Tomography to Understand Fluid-Fluid Interface Evolution in Porous Media for Carbon Sequestration Applications
… including Betti numbers and the corresponding Euler characteristic that are relevant to fluid connectivity for an air-water-sandstone system under ambient conditions. We aimed to investigate the effect of the saturation level of water and image resolution on the REV of the parameters …
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Derived categories of coherent sheaves on rational homogeneous manifolds
… $K$-group $K_{\circ}(X)$ given by the Euler characteristic with respect to the basis formed by the classes of structure sheaves of Schubert varieties in $X$; this matrix is conjugate to the Gram matrix of a complete exceptional sequence. Section 3 contains a proof of theorem 3.2.7 which …
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Solitons and dualities in 2+1 dimensions
… space of this quantum mechanics (that is, the Euler characteristic of the relevant quantum line bundle on the moduli space) in the case of $U(N_c)$ gauge theory with $N_f$ fundamental flavours at arbitrary Chern--Simons level, $\lambda$, compactified on an arbitrary closed Riemann surface. We …