The homology of a free loop space
نویسندگان
چکیده
منابع مشابه
Free loop space and homology
The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic objects, and we provide the various steps of the proofs, which are scattered around in the literature. This paper can be seen as a companion to the paper “Cycl...
متن کاملThe Cohomology Ring of the Free Loop Space of a Wedge of Spheres and Cyclic Homology
We investigate the cohomology of the free loop space of a one point union of a three-sphere with itself. The even dimensional subalgebra is not free and relations are presented explicitly. This algebra may also be identified as the cyclic homology of a “null algebra”. L’anneau de cohomologie de l’espace de lacets libres d’un bouquet de sphères et l’homologie cyclique. Résumé – Nous étudions l’a...
متن کاملTopological Hochschild Homology of Thom Spectra and the Free Loop Space
We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f : X → BF , where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identifies the topological Hochschild h...
متن کاملHomology Operations on a New Infinite Loop Space
Boyer et al. [1] defined a new infinite loop space structure on the space Mq = fTn>i ^(Z> 2/i) such that the total Chern class map BU —► Mq is an infinite loop map. This is a sort of Riemann-Roch theorem without denominators: for example, it implies Fulton-MacPherson's theorem that the Chem classes of the direct image of a vector bundle E under a given finite covering map are determined by the ...
متن کاملAlgebraic Structure in the Loop Space Homology Bockstein Spectral Sequence
Let X be a finite, n-dimensional, r-connected CW complex. We prove the following theorem: If p ≥ n/r is an odd prime, then the loop space homology Bockstein spectral sequence modulo p is a spectral sequence of universal enveloping algebras over differential graded Lie algebras.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.147.311