相关论文: Small Exotic 4-manifolds with b_2^+=3

We obtain constraints on the topology of families of smooth $4$-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation…

We introduce blow-up and blow-down operations for generalized complex 4-manifolds. Combining these with a surgery analogous to the logarithmic transform, we then construct generalized complex structures on nCP2 # m \bar{CP2} for n odd, a…

We give an explicit construction of vertex-transitive tight triangulations of $d$-manifolds for $d\geq 2$. More explicitly, for each $d\geq 2$, we construct two $(d^2+5d+5)$-vertex neighborly triangulated $d$-manifolds whose vertex-links…

It is well known that for any exotic pair of simply connected closed oriented 4-manifolds, one is obtained from the other by twisting a compact contractible submanifold via an involution on the boundary. By contrast, here we show that for…

We construct infinite families of abstract regular polytopes of type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain…

A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by…

We construct infinitely many smooth 4-manifolds which are homotopy equivalent to $S^2$ but do not admit a spine, i.e., a piecewise-linear embedding of $S^2$ which realizes the homotopy equivalence. This is the remaining case in the…

We study closed orientable manifolds whose topological complexity is at most 3 and determine their cohomology rings. For some of admissible cohomology rings we are also able to identify corresponding manifolds up to homeomorphism.

We construct an invariant of open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R^4 for which the invariant is non-trivial, showing that X is an exotic R^4.

We construct explicit maximal symplectic packings of minimal rational and ruled symplectic 4-manifolds by few balls in a very simple way.

Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We…

We construct smooth manifolds with order two $\pi_1$ and even intersection forms which are irreducible, meaning they do not decompose into non-trivial connected sums. Their intersection forms being even implies that their universal covers…

We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.

Let M be a 4-manifold with residually finite fundamental group G having b_1(G) > 0. Assume that M carries a symplectic structure with trivial canonical class K = 0 in H^2(M). Using a theorem of Bauer and Li, together with some classical…

We construct a connected cubic nonnormal Cayley graph on $\mathrm{A}_{2^m-1}$ for each integer $m\geqslant4$ and determine its full automorphism group. This is the first infinite family of connected cubic nonnormal Cayley graphs on…

We classify all simply connected Riemannian manifolds whose isotropy groups act with cohomogeneity less than or equal to two.

We build a non-compact, orientable, hyperbolic four-manifold of finite volume that does not admit any spin structure.

We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a…

We construct several infinite families of nonnegatively curved manifolds of low cohomogeneity and small dimension which can be distinguished by their cohomology rings. In particular, we exhibit an infinite family of eight-dimensional…

We construct an infinite family of topologically slice 2--component boundary links $\ell_i$, none of which is smoothly concordant to a split link, such that $g_4(\ell_i)=i$.