BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR<br><div class="gmail_quote"><div class="gmail_quote"><br>This week, we will have our final seminar of the semester as well as our fourth and final lecturer in our <b>Dean's Speaker Series in Geometry and Topology</b>, Ayelet Lindenstrauss of Indiana.<br>
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<br><i>Date:</i> Thursday, May 12, 2011<br>
<i>Time:</i> 2:50-3:50pm<br><i>Place:</i> Library North 2205 followed by coffee/tea in the Anderson Reading Room.<br>
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<i>Speaker:</i> Ayelet Lindenstrauss (Indiana)<br>Title: K-theory of formal power series<br><div><i></i>
<i><br>Abstract: </i>(joint with Randy McCarthy)<br><br>We study the algebraic K-theory of parametrized endomorphisms of a unital ring R with coefficients in a simplicial R-bimodule M, and compare it with the algebraic K-theory of the ring of formal power series in M over R.<br>
<br>Waldhausen defined an equivalence from the suspension of the reduced Nil K-theory of R with coefficients in M to the reduced algebraic K-theory of the tensor algebra T_R(M). Extending Waldhausen's map from nilpotent endomorphisms to all endomorphisms, our map has to land in the ring of formal power series rather than in the tensor algebra, and is no longer in general an equivalence (it is an equivalence when the bimodule M is connected). Nevertheless, the map shows a close connection between its source and its target: it induces an equivalence on the Goodwillie Taylor towers of the two (as functors of M, with R fixed), and allows us to give a formula for the suspension of the invariant W(R;M) (which can be thought of as Witt vectors with coefficients in M, and is what the Goodwillie Taylor tower of the source functor converges to) as the inverse limit, as n goes to infinity, of the reduced algebraic K-theory of T_R(M)/ (M^n).<br>
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