143 lines
3.5 KiB
Common Lisp
143 lines
3.5 KiB
Common Lisp
;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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(IN-PACKAGE #:cat)
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(provide "whitehead")
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;;;
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;;; Z
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;;;
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(DEFUN Z-WWHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z-n (k-z n))
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(idnt (bspn k-z-n))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z-n)
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(type gmsm idnt)
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(type homotopy-equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask dmns) idnt)
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(z-cocycle-gbar n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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(DEFUN Z-WHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z-n-1 (k-z (1- n)))
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(idnt (bspn k-z-n-1))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z-n-1)
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(type gmsm idnt)
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(type homotopy-equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask (1- dmns)) idnt)
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(z-cocycle-gbar-head n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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(DEFUN Z-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss))
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(the fibration
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(build-smmr
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:sorc smst :trgt (k-z (1- n)) :degr -1
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:sintr (z-whitehead-sintr smst n chml-clss)
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:orgn `(z-whitehead ,smst))))
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;;;
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;;; Z/2Z
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;;;
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(DEFUN Z2-WWHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z2-n (k-z2 n))
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(idnt (bspn k-z2-n))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z2-n)
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(type gmsm idnt)
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(type homotopy-equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask dmns) idnt)
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(z2-cocycle-gbar n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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(DEFUN Z2-WHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z2-n-1 (k-z2 (1- n)))
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(idnt (bspn k-z2-n-1))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z2-n-1)
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(type gmsm idnt)
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(type homotopy-equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask (1- dmns)) idnt)
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(z2-cocycle-gbar-head n dmns
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(gmsm-cocycle face n dmns gmsm
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chml-clss)))))
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(the sintr #'rslt)))
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(DEFUN Z2-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss))
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(the fibration
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(build-smmr
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:sorc smst :trgt (k-z2 (1- n)) :degr -1
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:sintr (Z2-whitehead-sintr smst n chml-clss)
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:orgn `(Z2-whitehead ,smst))))
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