Mathematical Sciences: Calculus of Funtors and Pseudo-Isotopy Theory

的任意两连通映射的相对伪合痕 空间将通过“函子演算”来研究， 一般同伦理论的方法，这是发明的 主要研究者主要是为了这个目的。 一个重点 将致力于完善微积分。 另一个将在 计算相对代数K-理论的一般问题 幂零理想或连通理想， 同调或S1-等变同伦。 这项研究的进展 将应用于微妙的几何问题， 变形的几何空间称为流形，其中， 理论物理学的转折影响研究。

The relative pseudoisotopy of any two-connected map of spaces will be studied by means of the "calculus of functors," a general homotopy-theoretic method which was invented by the principal investigator primarily for this purpose. One emphasis will be on refining this calculus. Another will be on the general problem of computing the relative algebraic K-theory of a nilpotent or connected ideal in terms of some sort of cyclic homology or S1-equivariant homotopy. Advances in this research will have application to subtle geometric questions about deformations of geometric spaces known as manifolds, which in turn impact research in theoretical physics.