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.
Derives an index formula for families of end-periodic Dirac operators.
Paper extends variational formula for Bismut-Cheeger eta form, proving key theorems in K-theory.
New Hessian estimates for heat equations on manifolds.
Paper generalizes spectral flow formulas for compact Lie group actions.
Bismut and Zhang computed the ratio of the Ray-Singer and the combinatorial torsions corresponding to non-unitary representations of the fundamental group. In this note we show that for representations which belong to a connected component containing a unitary representation the Bismut-Zhang formula follows rather easi…
Analytic surgery and gluing formula for torsion forms in fiber bundles.
We present an alternate proof of the Bismut-Zhang localization formula for -invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.
Paper establishes loop space T-duality formulae and refines earlier work.
We give a new and detailed proof of the variation formulas for the equivariant Ray-Singer metric, which are originally due to J.M. Bismut and W. Zhang.
Wave trace singularity formula for fibre bundles generalizes Poisson summation.
About 15 years ago, Bismut gave a natural construction of a Hodge theory for a hypoelliptic Laplacian acting on the total space of the cotangent bundle of a Riemannian manifold. This operator interpolates between the classical elliptic Laplacian on the base and the generator of the geodesic flow. We will describe recen…
In this paper, using the Greiner's approach to heat kernel asymptotics, we give new proofs of the equivariant Gauss-Bonnet-Chern formula and the variation formulas for the equivariant Ray-Singer metric, which are originally due to J. M. Bismut and W. Zhang.
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.
We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revi…
In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that the metrics have product structures near the cutting hypersurface.
Generalizes double transgression formulas on complex manifolds.
In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta forms with respect to the composition of two submersions.
Paper studies stability of generalized Ricci solitons with mathematical rigor.
This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "`a la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable tor…
Formula for analytic torsion forms in fibrations by projective curves.
In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern chara…
The paper studies harmonic complex structures and special metrics on Sasakian manifolds.
Bismut Einstein metrics on complex manifolds are Kähler Einstein or Bismut Ricci flat.
Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of …
Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.
We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, althou…
We generalize the transgression formula for the eta form of Bismut, Cheeger and Berline, Getzler, Vergne for vertical Dirac operators on a fibre bundle with odd dimensional fibres where the Dirac operators have locally at most one eigenvalue of multiplicity one crossing zero transversally.
Novel analysis of generalized Ricci solitons leads to stability results and deformations.
The paper classifies Bismut Kähler-like manifolds in dimensions 4 and 5.
The paper derives inequalities and formulas for generalized Ricci flow.
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics for stochastic volatility models with jumps. To this end one needs so…
Study SKT and CYT manifolds with parallel Bismut torsion.
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …
We extend the adiabatic limit formula for eta-invariants by Bismut-Cheeger and Dai to Seifert fibrations. Our formula contains a new contribution from the singular fibres that takes the form of a generalised Dedekind sum. As an application, we compute the Eells-Kuiper and t-invariants of certain cohomogeneity one manif…
A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module \ over a Riemannian manifold . Recently, this formula has been generalized to arbitrary Dirac operators [2]. In this …
Classifies simply-connected pluriclosed manifolds with parallel Bismut torsion.
The study characterizes Hermitian manifolds with parallel Bismut-Strominger torsion.
Characterizes Hermitian manifolds with Bismut parallel torsion.
Holonomy group of Bismut connection on Vaisman manifolds is studied.
New homogeneous manifolds with invariant Bismut Ricci flat connections are constructed.
Study on balanced Hermitian threefolds with parallel Bismut torsion.
Study Bismut-Griffiths-positivity in non-Kähler manifolds under Hermitian curvature flows.
Study Bismut connection curvatures and solve Yamabe and Calabi-Yau problems.
New insights prevent certain types of metrics on compact spaces.
Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a `resolution' in terms of a fibration, we construct a pseudodifferential calculus generalizing the fibred cusp calculus of Mazzeo and Melrose. In particular, we introduce certain symbols leading to a simple descripti…
Study on Hermitian metrics on Lie algebras with specific ideals.
We define the geometric complex associated to a Morse-Bott-Smale vector field, cf. [Austin-Braam, 1995], and its associated spectral sequence. We prove an extension of the Bismut-Zhang theorem to Morse-Bott-Smale functions. The proof is based on the Bismut-Zhang theorem for Morse-Smale functions, see [Bismut-Zhang, 199…