A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Note on new cancellation formulas for manifolds.
Study modular forms over Γ^0(2) and anomaly cancellation formulas.
We give a direct proof of a cancellation formula raised in [7] on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among these cancellation formulas are discussed.
For even dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas.
New anomaly formulas from E8 bundles.
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas
New modular forms for anomaly cancellation formulas on any dimensional manifolds.
New anomaly cancellation formulas for E8*E8*E8 gauge group.
New anomaly formulas derived from bundles.
SL(2,Z) forms lead to new anomaly formulas.
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaumé and Witten in dimensions 2, 6 and 10 (\cite{AW}) as special cases. …
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
This paper examines the value of a cancellable European option in a finite time horizon setting. The specifications of this generalized European option allow the seller to cancel the option at any point in time for a fixed penalty paid directly to the holder. Here, we provide an explicit valuation formula for the Europ…
Abstract: Generalizes modular forms to family case and finds new anomaly cancellation formulas.
By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin manifolds. Especially, we get twisted Rokhlin congruences for dimensional spi…
The paper extends elliptic genus and proves anomaly cancellation formulas for almost complex manifolds.
New formulas derived from modular forms for manifold indices.
The paper defines new modular forms from almost complex manifolds and derives anomaly cancellation formulas.
In this paper, we generalize the anomaly cancellation formulas in \cite{AW, Liu1, HZ2} to the cases that an auxiliary bundle as well as a complex line bundle are involved with no conditions on the first Pontryagin forms being assumed.
By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz operators on dimensional spin manifolds and some congruent formulas on ch…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We also get some twisted anomaly cancellation formulas on some odd dimensional manifol…
It has been shown that the Alvarez-Gaum-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…
New cubic forms linked to η-invariants and mod 2 indices.
We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula…
We survey the Hirzebruch signature theorem as a special case of the Atiyah-Singer index theorem. The family version of the Atiyah-Singer index theorem in the form of the Riemann-Roch-Grothendieck-Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of ellipti…
We generalize the "miraculous cancellation" formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruence formulas of Ochanine [O1], Finashin [F] and Zha…
New formula recovers degree of colored Jones polynomials for pretzel knots.
In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group and the Hořava-Witten anomaly factorization formula for the gauge group can be derived through modular forms of weight 14. This answers a question of J. H. Schwarz. We also establish generalizati…
We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial eleme…
New elliptic genera defined for spin manifolds.
This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the asset value. We first consider a vanilla insurance contract whereby the protectio…
The order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order-driven markets. We investigate the dynamics of order cancelation by studying the statistical properties of inter-cancelation durations defined as the waiting times between consecutive order cancelatio…
Order cancellation process plays a crucial role in the dynamics of price formation in order-driven stock markets and is important in the construction and validation of computational finance models. Based on the order flow data of 18 liquid stocks traded on the Shenzhen Stock Exchange in 2003, we investigate the empiric…
New proof shows Cohen-Lyndon property for non-metric small-cancellation.
We establish the cancellation of the first terms in the diagonal asymptotic expansion of the restriction to the -forms of the Bergman kernel associated to the spin Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a c…
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place without canceling each other out and to model triple junctions without introducing …
Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less understood. There are two positions associated with a cancellation, that is, the price…
We prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the Möbius band admits no cancellative continuous binary operation. This answers a question posed by the second author in 2010.
The classification of isoparametric hypersurfaces with four principal curvatures in spheres in [2] hinges on a crucial characterization, in terms of four sets of equations of the 2nd fundamental form tensors of a focal submanifold, of an isoparametric hypersurface of the type constructed by Ferus, Karcher and Münzner. …
In this paper, we derive an asymptotic formula for the number of conjugacy classes of elements in a class of statistically convex-cocompact actions with contracting elements. Denote by (resp. ) the set of (resp. primitive) conjugacy classes of pointed length at most for a basep…
We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversi…
Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomised) stopping time, rather than instantly at an ordinary stopping time. Allo…
The paper proves smoothness of transition layers in the Allen-Cahn equation.
We establish the cancellation of the first |2j-q| terms in the diagonal asymptotic expansion of the restriction to the (0, 2j)-forms of the Bergman kernel associated to the modified spin^c Dirac operator on high tensor powers of a line bundle with mixed curvature twisted by a (non necessarily holomorphic) complex vecto…
Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.
We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the…
We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays a…
Introduces a theorem for groups acting on trees.