Mathematical Sciences: Calculus of Funtors and Pseudo-Isotopy Theory

任何两连通空间映射的相对伪同位素将通过“函子演算”来研究，这是一种由主要研究者为此目的发明的一般同伦理论方法。重点之一将是改进这个演算。另一个是关于计算幂零或连通理想的相对代数k理论的一般问题在某种循环同伦或s1等变同伦方面。这一研究的进展将应用于有关几何空间（即流形）变形的微妙几何问题，进而影响理论物理的研究。

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.