By Selman Akbulut (auth.), Ilia Itenberg, Burglind Jöricke, Mikael Passare (eds.)

The contributions during this volume—dedicated to the paintings and mathematical pursuits of Oleg Viro at the social gathering of his sixtieth birthday—are invited papers from the Marcus Wallenberg symposium and concentrate on study issues that bridge the distance between research, geometry, and topology. The encounters between those 3 fields are frequent and sometimes offer impetus for significant breakthroughs in applications.

Topics lined contain new advancements in low-dimensional topology on the topic of invariants of hyperlinks and 3- and 4-dimensional manifolds and the new advances made in algebraic, advanced, symplectic, and tropical geometry.

This assortment is meant for graduate scholars and researchers in research, geometry, and topology, specifically these whose zone of research applies to 2 or extra of those fields.

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**Additional resources for Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthday of Oleg Viro**

**Sample text**

The reader should contrast this with [A5], where examples of other knot pairs K, L ⊂ S3 are given (one is a slice; the other is not a slice) such that attaching 2-handles to B4 along K, L gives diffeomorphic four-manifolds, as in Fig. 9. Fig. 8 Exotic manifold pairs Exotic Structures on Smooth Four-Manifolds 7 Fig. 9 Diffeomorphic manifold pairs 2 PALFs It turns out that Stein manifolds admit finer structures as primitives. They are “positive allowable Lefschetz fibrations” over the 2-disk, where the regular fibers are surfaces F with boundaries; in [AO1], we called them PALFs.

Let L be a (rationally null-homologous) fibered link in M. Suppose K is a component of L for which the fibers in the fibration approach as (r, s)-curves (in some framing on K). Let L be the link formed from L by replacing K by the (p, q)-cable of K, where p = ±1, 0 and (p, q) = (kr, ks) for any k ∈ Q. Then L is fibered. Moreover, the Euler characteristic of the new fiber is χ (Σnew ) = 1 (|p|χ (Σold ) + |ps − qr|(1 − |p|)), gcd(p, r) where Σnew is the fiber of L and Σold is the fiber of L. The multiplicity of each component of the cable of K is gcd p(rq − sp) r , gcd(p, r) gcd(p, r) gcd(p, q) and the order of Σnew along each component of the cable of K is r .

Akbulut and K. Yasui Knotting corks, Jour. of Topology, 2(4) (2009), 823–839. [ADK] D. Auroux, S. K. Katzarkov, Singular Lefschetz pencils, GT 9 (2005), 1043–1114. [AEMS] A. Akhmedov, J. B. Etnyre, T. E. Mark, and I. 3932. [Ar] M. F. Arikan, On support genus of a contact structure, Journal of G¨okova Geometry Topology, 1 (2007), 96–115. [B1] I. Baykur, K¨ahler decomposition of 4-manifolds, arXiv:0601396v2 [B2] I. 3139. [Bo] S. Boyer, Simply-connected 4-manifolds with a given boundary, Trans. Amer.