# Abstract/Details

## Fixed point indices, transfers and path fields

1990 1990

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### Abstract (summary)

Let $V$ be a vector field on a compact differentiable manifold $M$. Assume $V$ has no zeros on the boundary $\partial M$. Marston Morse discovered in 1929 an interesting formula relating the indices of the vector field $V$ and of a vector field $\partial\underline{\enspace} V$ defined on a part of the boundary to the Euler characteristic of $M:{\rm Ind}(V) + {\rm Ind} (\partial\underline{\enspace} V)$ = $\chi(M)$; this formula generalizes the well-known Poincare-Hopf Index Theorem for vector fields. In this work we obtain analogous formulas, $I(f)$ + $I(rf\vert\sb{\partial\underline{\enspace} M}$ = $\chi(M)$ for fixed point indices, $t\sb{rf}$ = $t\sb{f}\ \circ\ \breve i\sbsp{1}{\*}+t\sb{\partial\underline{\enspace} f}\ \circ\ \breve i\sp{\*}\ \circ\ \breve i\sbsp{2}{\*}$ for fixed point transfers and Ind($\sigma$) + Ind($\partial\underline{\enspace}\sigma$) = $\chi(M)$ for path field indices.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Fixed point indices, transfers and path fields
Author
Benjamin, Chen-Farng
Number of pages
48
Publication year
1990
Degree date
1990
School code
0183
Source
DAI-B 51/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Gottlieb, Daniel H.
University/institution
Purdue University
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9104600
ProQuest document ID
303850424