Clemens-Schmid exact sequence in characteristic p

For a semistable family of varieties over a curve in characteristic $p$, we prove the existence of a "Clemens-Schmid type" long exact sequence for the $p$-adic cohomology. The cohomology groups appearing in such a long exact sequence are defined locall

The Birman exact sequence for 3-manifolds

We study the Birman exact sequence for compact $3$--manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and non-orientable ones.Comment: 30 pages, no figures. v2: Major re-write following referee suggestions. To appear in Bull. Lond. Math. Soc.; v1: This paper gives an alternative, more algebraic, proof of the main result of arXiv:1310.7884 (with less exposition

A Coboundary Morphism For The Grothendieck Spectral Sequence

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Comment: 18 page

On 0-cycles with modulus

Given a smooth surface $X$ over a field and an effective Cartier divisor $D$, we provide an exact sequence connecting $CH_0(X,D)$ and the relative $K$-group $K_0(X,D)$. We use this exact sequence to answer a question of Kerz and Saito whenever $X$ is a resolution of singularities of a normal surface. This exact sequence is used to show that the localization sequence for ordinary Chow groups does not extend to Chow groups with modulus.Comment: Title changed, with minor revision. Final version, to appear in Algebra Number Theory (2015

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification