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Serre spectral sequence of a product added

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Serre-Whitehead spectral sequence added
Problems solved in file homotopy (reductions are now compatible with filtrations)
This commit is contained in:
Ana Romero 2019-07-11 13:52:38 +02:00
parent 071d64166d
commit 086bbc82bc
2 changed files with 94 additions and 15 deletions
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12
src/anromero/homotopy.lisp
View File

@ -119,21 +119,24 @@
(cond ((equal (car list) 1) (let* ((ch (chml-clss chcm indx))
(fib (z-whitehead chcm ch))
(ft (fibration-total fib)))
(if (endp (cdr list)) ft
(progn
(kill-epis ft 1 indx)
(construct-space-iterative ft (cdr list) indx))))
(construct-space-iterative ft (cdr list) indx)))))
((equal (car list) 2) (let* ((ch (chml-clss chcm indx))
(fib (z2-whitehead chcm ch))
(ft (fibration-total fib)))
(if (endp (cdr list)) ft
(progn
(kill-epis ft 1 indx)
(construct-space-iterative ft (cdr list) indx))))
(construct-space-iterative ft (cdr list) indx)))))
(t (let* ((ch (chml-clss chcm indx))
(fib (zp-whitehead (car list) chcm ch))
(ft (fibration-total fib)))
(if (endp (cdr list)) ft
(progn
(kill-epis ft 1 indx)
(construct-space-iterative ft (cdr list) indx))))
(kill-epis ft 1 indx)
(construct-space-iterative ft (cdr list) indx)))))
)))
@ -205,3 +208,4 @@

97
src/anromero/spectral-sequences.lisp
View File

@ -1581,7 +1581,7 @@
l))))))
;; Function that returns the matrix (as a list of lists) of the differential
;; Method that returns the matrix (as a list of lists) of the differential
;; d: E^r_{p,q} --> E^r_{p-r,q+r-1}, using the effective homology
;; when the complex is not of finite type.
(DEFMETHOD SPECTRAL-SEQUENCE-DIFFERENTIAL-MATRIX ((ss SPECTRAL-SEQUENCE) r p q)
@ -1606,28 +1606,65 @@
l))))))
;; Funcion that constructs the Serre spectral sequence associated with a fibration f
;; Function that constructs the Serre spectral sequence associated with a fibration f
;; Returns an object of the class Spectral-sequence
(DEFUN SERRE-SPECTRAL-SEQUENCE (f)
(DEFUN SERRE-SPECTRAL-SEQUENCE-FIBRATION (f)
(declare (type fibration f))
(let* ((fltrcm (fibration-total f))
(ecc (rbcc (efhm fltrcm))))
(declare (type simplicial-set fltrcm)
(type chain-complex ecc))
(progn
(change-chcm-to-flcc fltrcm crpr-flin 'crpr-flin)
(change-chcm-to-flcc ecc tnpr-flin 'tnpr-flin)
(build-ss fltrcm `(Serre-Spectral-Sequence ,f)))))
(the spectral-sequence
(build-ss fltrcm `(Serre-Spectral-Sequence ,f))))))
;; Function that constructs the Serre spectral sequence associated with a simplicial set
;; which is given as a (twisted) cartesian product. Returns an object of the class Spectral-sequence
(DEFUN SERRE-SPECTRAL-SEQUENCE-PRODUCT (x)
(declare (type simplicial-set x))
(let ((ecc (rbcc (efhm x))))
(declare (type chain-complex ecc))
(progn
(change-chcm-to-flcc x crpr-flin 'crpr-flin)
(change-chcm-to-flcc ecc tnpr-flin 'tnpr-flin)
(the spectral-sequence
(build-ss x `(Serre-Spectral-Sequence ,x))))))
;; Funcion that constructs the Eilenberg-Moore spectral sequence associated with a (1-reduced)
;; Function that constructs the Serre spectral sequence of the first fibration of the
;; Whitehead tower of fibrations of a 1-reduced simplicial set
(DEFUN SERRE-WHITEHEAD-SPECTRAL-SEQUENCE (x)
(let* (;; we obtain the first non null homology group
(first-non-null (first-non-null-homology-group x 20))
(degr (1+ first-non-null))
(hom (homology-format x degr))
(ft (construct-space-iterative x (split-components hom) degr)))
(declare (fixnum first-non-null degr)
(type string hom)
(type simplicial-set ft))
(the spectral-sequence
(serre-spectral-sequence-product ft))))
;; Function that constructs the Eilenberg-Moore spectral sequence associated with a (1-reduced)
;; simplicial set X
;; Returns an object of the class Spectral-sequence
(DEFUN EILENBERG-MOORE-SPECTRAL-SEQUENCE (x)
(declare (type simplicial-set x))
(let* ((ox (loop-space x))
(ecc (rbcc (efhm OX))))
(declare
(type simplicial-set ox)
(type chain-complex ecc))
(progn
(change-chcm-to-flcc ecc cobar-flin 'cobar-flin)
(build-ss ecc `(Eilenberg-Moore-Spectral-Sequence ,x)))))
(the spectral-sequence
(build-ss ecc `(Eilenberg-Moore-Spectral-Sequence ,x))))))
#|
@ -1638,7 +1675,9 @@
(setf F3 (z-whitehead s3 k3)))
(setf ss1 (serre-spectral-sequence f3))
(setf ss1 (serre-spectral-sequence-fibration f3))
(spectral-sequence-group ss1 2 0 2)
(setf r 2)
@ -1660,10 +1699,10 @@
(setf x (loop-space (sphere 3)))
(setf ss2 (eilenberg-moore-spectral-sequence x))
(dotimes (n 6)
(dotimes (p (1+ n))
(let ((q (+ n p)))
(print-spsq-group ss2 1 (- p) q))))
;;(dotimes (n 6)
;; (dotimes (p (1+ n))
;; (let ((q (+ n p)))
;; (print-spsq-group ss2 1 (- p) q))))
(spectral-sequence-differential-matrix ss2 1 -2 8)
(spectral-sequence-differential-of-one-element ss2 1 -2 8 '(1 0 0))
@ -1676,6 +1715,42 @@
(spectral-sequence-differential-matrix ss2 1 -2 6)
(cat-init)
(setf s3 (sphere 3))
(setf ss3 (serre-whitehead-spectral-sequence s3))
(spectral-sequence-group ss3 2 0 2)
(dotimes (n 8)
(dotimes (p (1+ n))
(let ((q (- n p)))
;;(print-spsq-group ss3 r p q)
(format t "Spectral sequence E^~D_{~D,~D}" r p q)
(print (spectral-sequence-group ss3 r p q))
(terpri))))
(spectral-sequence-differential-matrix ss3 3 3 0)
(spectral-sequence-differential-matrix ss3 3 3 2)
(spectral-sequence-differential-matrix ss3 3 3 4)
(cat-init)
(setf s3 (sphere 3) s2 (sphere 2))
(setf ss4 (serre-spectral-sequence-product (crts-prdc s3 s2)))
(dotimes (n 8)
(dotimes (p (1+ n))
(let ((q (- n p)))
;;(print-spsq-group ss1 r p q)
(format t "Spectral sequence E^~D_{~D,~D}" r p q)
(print (spectral-sequence-group ss4 r p q))
(terpri))))
|#