Homotopy and Cohomology in Algebraic Topology

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We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of…

• CAN KOZÇAZ

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In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding component…

The survey gives an overview of the achievements in topology of real algebraic varieties in the direction initiated in the early 70th by V.I.Arnold and V.A.Rokhlin. We make an attempt to systematize the principal results in the subject. After an exposition of general tools and results, special attention is paid to sur…

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In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.

In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids…

• NESLİHAN GÜGÜMCÜ

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• İREM KÜPELİ ERKEN

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• CENGİZHAN MURATHAN

For every integer g ≥ 2 there exist infinitely many pairwise nonhomeomorphic smooth 4-manifolds admitting genus-g Lefschetz fibration over S2 but not carrying any complex structure. This extends a recent result of Ozbagci and Stipsicz.

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over $S^2$. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not n…