This ebook is an advent to combinatorial torsions of mobile areas and manifolds with precise emphasis on torsions of three-d manifolds. the 1st chapters hide algebraic foundations of the speculation of torsions and numerous topological structures of torsions as a result of okay. Reidemeister, J.H.C. Whitehead, J. Milnor and the writer. We additionally talk about connections among the torsions and the Alexander polynomials of hyperlinks and 3-manifolds. The 3rd (and final) bankruptcy of the publication bargains with so-called subtle torsions and the comparable extra buildings on manifolds, in particular homological orientations and Euler constructions. As an program, we provide a building of the multivariable Conway polynomial of hyperlinks in homology 3-spheres. on the finish of the publication, we in short describe the hot result of G. Meng, C.H. Taubes and the writer at the connections among the sophisticated torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed toward scholars, expert mathematicians and physicists drawn to combinatorial points of topology and/or in low dimensional topology. the required historical past for the reader comprises the ordinary fundamentals of topology and homological algebra.
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