on the exponential decay of the n point correlation functions and the analyticity of the pressure the goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n point correlation functions for certain unbounded models of kac type the methods are based on estimating higher order derivatives of the solution of the witten laplacian equation on 1 forms associated with the hamiltonian of the system we also provide a formula for the taylor coefficients of the pressure that is suitable for a direct proof of the analyticity

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

separated solutions of logistic equation with nonperiodic harvesting abstract in this paper we study logistic equations with non periodic harvesting we introduce the notion of separated solutions and then show the existence of upper and lower solutions that are separated we further show that the lower solution is unique and all solutions that start above the lower solution tend to each other while solutions that start below the lower solution blow up in finite time

n 2 topological yang mills theory on compact kahler surfaces we study a topological yang mills theory withn 2 fermionic symmetry our formalism is a field theoretical interpretation of the donaldson polynomial invariants on compact kahler surfaces we also study an analogous theory on compact oriented riemann surfaces and briefly discuss a possible application of witten s non abelian localization formula to the problems in the case of compact kahler surfaces

correlation at low temperature ii asymptotics the present paper is a continuation of ref 4 where the truncated two point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature under a weak coupling assumption in this paper we compute the asymptotics of the correlation function as the temperature goes to zero this paper thus extends ref 3 in two directions the hamiltonian function is allowed to have several local minima other than a unique global minimum and we do not require translation invariance of the hamiltonian function we are in particular able to handle spin systems on a general lattice

nahm s transformation for instantons we describe in mathematical detail the nahm transformation which maps anti self dual connections on the four torus s1 4 onto anti self dual connections on the dual torus this transformation induces a map between the relevant instanton moduli spaces and we show that this map is a hyperkahler isometry

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

on the correlation for kac like models in the convex case the aim of this paper is to stu the behavior asm tends to of a family of measures exp m x dx m on m where m is a potential on m which is a perturbation in a suitable sense of the harmonic potential j x j 2

free involutions on s 1 s n topological free involutions on s 1 s n are classified up to conjugation weprovethatthisisthesameasclassifyingquotientmanifoldsuptohomeomorphism there are exactly four possible homotopy types of such quotients and surgery theory is used to classify all manifolds within each homotopy type

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

on separated solutions of logistic population equation with harvesting abstract we provide a surprising answer to a question raised in s ahmad and a c lazer 2 and extend the results of that paper

witten laplacian method for the decay of correlations the aim of this paper is to apply direct methods to the study of integrals that appear naturally in statistical mechanics and euclidean field theory we provide weighted estimates leading to the exponential decay of the two point correlation functions for certain classical convex unbounded models the methods involve the study of the solutions of the witten laplacian equations associated with the hamiltonian of the system

correlation at low temperature i exponential decay abstract the present paper generalizes the analysis in ann h poincare 1 2000 59 math j ams 8 1997 123 of the correlations for a lattice system of real valued spins at low temperature the gibbs measure is assumed to be generated by a fairly general hamiltonian function with pair interaction the novelty as compared to 2 20 is that the single site self energies of the spins are not required to have only a single local minimum and no other extrema our derivation of exponential decay of correlations goes through the spectral analysis of a deformed laplacian closely related to the witten laplacian studied in 2 20 we prove that this laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations

metrics on the moduli spaces of instantons over euclidean 4 space we prove that the natural hyper kahler metrics on the moduli space of chargek instantons over euclidean four space and on the space of adhm matrices coincide we use this to deduce formulae relating expressions in the curvature of a connection to invariant polynomials in the adhm matrices corresponding to this connection these arise from consideration of the group of symmetries acting on the moduli spaces

smooth s cobordisms of elliptic 3 manifolds the main result of this paper states that a symplectic s cobordism of elliptic 3 manifolds is diffeomorphic to a product assuming a canonical contact structure on the boundary based on this theorem we conjecture that a smooth s cobordism of elliptic 3 manifolds is smoothly a product if its universal cover is smoothly a product we explain how the conjecture fits naturally into the program of taubes of constructing symplectic structures on an oriented smooth 4 manifold with b 1 from generic self dual harmonic forms the paper also contains an auxiliary result of independent interest which generalizes taubes theorem sw gr to the case of symplectic 4 orbifolds

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

on definite lattices bounded by integer surgeries along knots with slice genus at most 2 we classify the positive definite intersection forms that arise from smooth 4 manifolds with torsion free homology bounded by positive integer surgeries on the right handed trefoil a similar slightly less complete classification is given for the 2 5 torus knot and analogous results are obtained for integer surgeries on knots of slice genus at most two the proofs use input from yang mills instanton gauge theory and heegaard floer correction terms

orientability for gauge theories on calabi yau manifolds abstract we study orientability issues of moduli spaces from gauge theories on calabi yau manifolds our results generalize and strengthen those for donaldson thomas theory on calabi yau manifolds of dimensions 3 and 4 we also prove a corresponding result in the relative situation which is relevant to the gluing formula in dt theory

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

witten laplacian method for generalized models of kac type we first study the exponential decay of correlations for classical models of kac type using recent results j jon on spectral properties of witten laplacians their range of projections and brascamp lieb inequality integral equ oper theory 36 3 288 324 2000 10 1007 bf01213926 about the witten laplacians we improve the bounds obtained a lo witten laplacian methods for the decay of correlations j stat phys 132 2 355 396 2008 10 1007 s10955 008 9547 6 to justify the conjecture that the critical point in the d 1 dimensional kac model is given by c 1 4d we also provide a new approach for proving the exponential decay of the usual truncated correlations which is more direct than the existing ones in the sense that it does not use any cluster type expansions

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2