Elliptic GW invariants of blowups along curves and surfaces.
Hu, Jianxun, Zhang, Hou-Yang (2005)
International Journal of Mathematics and Mathematical Sciences
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Hu, Jianxun, Zhang, Hou-Yang (2005)
International Journal of Mathematics and Mathematical Sciences
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Erwan Brugallé, Nicolas Puignau (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Bryan, Jim, Pandharipande, Rahul (2001)
Geometry & Topology
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Yuka Kotorii (2014)
Fundamenta Mathematicae
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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.
Jim Bryan (1997)
Forum mathematicum
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Paolo Lisca (1995)
Inventiones mathematicae
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Su-Cheng Chang
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Sam Nelson (2014)
Fundamenta Mathematicae
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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Alessandro Paris, Alexandre Vinogradov (2011)
Open Mathematics
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All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential...
Taubes, Clifford Henry (1998)
Documenta Mathematica
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Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Dan Abramovich, Steffen Marcus, Jonathan Wise (2014)
Annales de l’institut Fourier
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We consider four approaches to relative Gromov–Witten theory and Gromov–Witten theory of degenerations: J. Li’s original approach, B. Kim’s logarithmic expansions, Abramovich–Fantechi’s orbifold expansions, and a logarithmic theory without expansions due to Gross–Siebert and Abramovich–Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov–Witten invariants...
C. T. C. Wall (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Nathan Geer (2014)
Banach Center Publications
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We show that the coefficients of the re-normalized link invariants of [3] are Vassiliev invariants which give rise to a canonical family of weight systems.
D. Kotschick, P. Lisca (1995)
Mathematische Annalen
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