By Vladimir Turaev

This booklet is an advent to combinatorial torsions of mobile areas and manifolds with particular emphasis on torsions of third-dimensional manifolds. the 1st chapters conceal algebraic foundations of the idea of torsions and diverse topological buildings of torsions because of okay. Reidemeister, J.H.C. Whitehead, J. Milnor and the writer. We additionally speak about connections among the torsions and the Alexander polynomials of hyperlinks and 3-manifolds. The 3rd (and final) bankruptcy of the e-book bargains with so-called sophisticated torsions and the comparable extra constructions on manifolds, particularly homological orientations and Euler constructions. As an software, we provide a development of the multivariable Conway polynomial of hyperlinks in homology 3-spheres. on the finish of the booklet, we in brief describe the new result of G. Meng, C.H. Taubes and the writer at the connections among the subtle torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed toward scholars, expert mathematicians and physicists attracted to combinatorial elements of topology and/or in low dimensional topology. the mandatory historical past for the reader comprises the straightforward fundamentals of topology and homological algebra.

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